高一必修1-2人教版数学所有公式
\u8dea\u6c42\u9ad8\u4e00\u4eba\u6559\u7248\u6570\u5b66\u5fc5\u4fee\u4e00\u3001\u5fc5\u4fee\u4e8c\u7684\u5b8c\u6574\u516c\u5f0f\u5927\u5168\uff01\uff01\uff01\u5e73\u65b9\u5173\u7cfb\uff1a
sin^2\u03b1\uff0bcos^2\u03b1\uff1d1
1\uff0btan^2\u03b1\uff1dsec^2\u03b1
1\uff0bcot^2\u03b1\uff1dcsc^2\u03b1
\u00b7\u79ef\u7684\u5173\u7cfb\uff1a
sin\u03b1=tan\u03b1\u00d7cos\u03b1
cos\u03b1=cot\u03b1\u00d7sin\u03b1
tan\u03b1=sin\u03b1\u00d7sec\u03b1
cot\u03b1=cos\u03b1\u00d7csc\u03b1
sec\u03b1=tan\u03b1\u00d7csc\u03b1
csc\u03b1=sec\u03b1\u00d7cot\u03b1
\u00b7\u5012\u6570\u5173\u7cfb\uff1a
tan\u03b1 \u00b7cot\u03b1\uff1d1
sin\u03b1 \u00b7csc\u03b1\uff1d1
cos\u03b1 \u00b7sec\u03b1\uff1d1
\u5546\u7684\u5173\u7cfb\uff1a
sin\u03b1/cos\u03b1\uff1dtan\u03b1\uff1dsec\u03b1/csc\u03b1
cos\u03b1/sin\u03b1\uff1dcot\u03b1\uff1dcsc\u03b1/sec\u03b1
\u76f4\u89d2\u4e09\u89d2\u5f62ABC\u4e2d,
\u89d2A\u7684\u6b63\u5f26\u503c\u5c31\u7b49\u4e8e\u89d2A\u7684\u5bf9\u8fb9\u6bd4\u659c\u8fb9,
\u4f59\u5f26\u7b49\u4e8e\u89d2A\u7684\u90bb\u8fb9\u6bd4\u659c\u8fb9
\u6b63\u5207\u7b49\u4e8e\u5bf9\u8fb9\u6bd4\u90bb\u8fb9,
\u00b7[1]\u4e09\u89d2\u51fd\u6570\u6052\u7b49\u53d8\u5f62\u516c\u5f0f
\u00b7\u4e24\u89d2\u548c\u4e0e\u5dee\u7684\u4e09\u89d2\u51fd\u6570\uff1a
cos(\u03b1+\u03b2)=cos\u03b1\u00b7cos\u03b2-sin\u03b1\u00b7sin\u03b2
cos(\u03b1-\u03b2)=cos\u03b1\u00b7cos\u03b2+sin\u03b1\u00b7sin\u03b2
sin(\u03b1\u00b1\u03b2)=sin\u03b1\u00b7cos\u03b2\u00b1cos\u03b1\u00b7sin\u03b2
tan(\u03b1+\u03b2)=(tan\u03b1+tan\u03b2)/(1-tan\u03b1\u00b7tan\u03b2)
tan(\u03b1-\u03b2)=(tan\u03b1-tan\u03b2)/(1+tan\u03b1\u00b7tan\u03b2)
\u00b7\u4e09\u89d2\u548c\u7684\u4e09\u89d2\u51fd\u6570\uff1a
sin(\u03b1+\u03b2+\u03b3)=sin\u03b1\u00b7cos\u03b2\u00b7cos\u03b3+cos\u03b1\u00b7sin\u03b2\u00b7cos\u03b3+cos\u03b1\u00b7cos\u03b2\u00b7sin\u03b3-sin\u03b1\u00b7sin\u03b2\u00b7sin\u03b3
cos(\u03b1+\u03b2+\u03b3)=cos\u03b1\u00b7cos\u03b2\u00b7cos\u03b3-cos\u03b1\u00b7sin\u03b2\u00b7sin\u03b3-sin\u03b1\u00b7cos\u03b2\u00b7sin\u03b3-sin\u03b1\u00b7sin\u03b2\u00b7cos\u03b3
tan(\u03b1+\u03b2+\u03b3)=(tan\u03b1+tan\u03b2+tan\u03b3-tan\u03b1\u00b7tan\u03b2\u00b7tan\u03b3)/(1-tan\u03b1\u00b7tan\u03b2-tan\u03b2\u00b7tan\u03b3-tan\u03b3\u00b7tan\u03b1)
\u00b7\u8f85\u52a9\u89d2\u516c\u5f0f\uff1a
Asin\u03b1+Bcos\u03b1=(A²+B²)^(1/2)sin(\u03b1+t)\uff0c\u5176\u4e2d
sint=B/(A²+B²)^(1/2)
cost=A/(A²+B²)^(1/2)
tant=B/A
Asin\u03b1-Bcos\u03b1=(A²+B²)^(1/2)cos(\u03b1-t)\uff0ctant=A/B
\u00b7\u500d\u89d2\u516c\u5f0f\uff1a
sin(2\u03b1)=2sin\u03b1\u00b7cos\u03b1=2/(tan\u03b1+cot\u03b1)
cos(2\u03b1)=cos²(\u03b1)-sin²(\u03b1)=2cos²(\u03b1)-1=1-2sin²(\u03b1)
tan(2\u03b1)=2tan\u03b1/[1-tan²(\u03b1)]
\u00b7\u4e09\u500d\u89d2\u516c\u5f0f\uff1a
sin(3\u03b1)=3sin\u03b1-4sin³(\u03b1)=4sin\u03b1\u00b7sin(60+\u03b1)sin(60-\u03b1)
cos(3\u03b1)=4cos³(\u03b1)-3cos\u03b1=4cos\u03b1\u00b7cos(60+\u03b1)cos(60-\u03b1)
tan(3\u03b1)=tan a \u00b7 tan(\u03c0/3+a)\u00b7 tan(\u03c0/3-a)
\u00b7\u534a\u89d2\u516c\u5f0f\uff1a
sin(\u03b1/2)=\u00b1\u221a((1-cos\u03b1)/2)
cos(\u03b1/2)=\u00b1\u221a((1+cos\u03b1)/2)
tan(\u03b1/2)=\u00b1\u221a((1-cos\u03b1)/(1+cos\u03b1))=sin\u03b1/(1+cos\u03b1)=(1-cos\u03b1)/sin\u03b1
\u00b7\u964d\u5e42\u516c\u5f0f
sin²(\u03b1)=(1-cos(2\u03b1))/2=versin(2\u03b1)/2
cos²(\u03b1)=(1+cos(2\u03b1))/2=covers(2\u03b1)/2
tan²(\u03b1)=(1-cos(2\u03b1))/(1+cos(2\u03b1))
\u00b7\u4e07\u80fd\u516c\u5f0f\uff1a
sin\u03b1=2tan(\u03b1/2)/[1+tan²(\u03b1/2)]
cos\u03b1=[1-tan²(\u03b1/2)]/[1+tan²(\u03b1/2)]
tan\u03b1=2tan(\u03b1/2)/[1-tan²(\u03b1/2)]
\u00b7\u79ef\u5316\u548c\u5dee\u516c\u5f0f\uff1a
sin\u03b1\u00b7cos\u03b2=(1/2)[sin(\u03b1+\u03b2)+sin(\u03b1-\u03b2)]
cos\u03b1\u00b7sin\u03b2=(1/2)[sin(\u03b1+\u03b2)-sin(\u03b1-\u03b2)]
cos\u03b1\u00b7cos\u03b2=(1/2)[cos(\u03b1+\u03b2)+cos(\u03b1-\u03b2)]
sin\u03b1\u00b7sin\u03b2=-(1/2)[cos(\u03b1+\u03b2)-cos(\u03b1-\u03b2)]
\u00b7\u548c\u5dee\u5316\u79ef\u516c\u5f0f\uff1a
sin\u03b1+sin\u03b2=2sin[(\u03b1+\u03b2)/2]cos[(\u03b1-\u03b2)/2]
sin\u03b1-sin\u03b2=2cos[(\u03b1+\u03b2)/2]sin[(\u03b1-\u03b2)/2]
cos\u03b1+cos\u03b2=2cos[(\u03b1+\u03b2)/2]cos[(\u03b1-\u03b2)/2]
cos\u03b1-cos\u03b2=-2sin[(\u03b1+\u03b2)/2]sin[(\u03b1-\u03b2)/2]
\u00b7\u63a8\u5bfc\u516c\u5f0f
tan\u03b1+cot\u03b1=2/sin2\u03b1
tan\u03b1-cot\u03b1=-2cot2\u03b1
1+cos2\u03b1=2cos²\u03b1
1-cos2\u03b1=2sin²\u03b1
1+sin\u03b1=(sin\u03b1/2+cos\u03b1/2)²
\u00b7\u5176\u4ed6\uff1a
sin\u03b1+sin(\u03b1+2\u03c0/n)+sin(\u03b1+2\u03c0*2/n)+sin(\u03b1+2\u03c0*3/n)+\u2026\u2026+sin[\u03b1+2\u03c0*(n-1)/n]=0
cos\u03b1+cos(\u03b1+2\u03c0/n)+cos(\u03b1+2\u03c0*2/n)+cos(\u03b1+2\u03c0*3/n)+\u2026\u2026+cos[\u03b1+2\u03c0*(n-1)/n]=0 \u4ee5\u53ca
sin²(\u03b1)+sin²(\u03b1-2\u03c0/3)+sin²(\u03b1+2\u03c0/3)=3/2
tanAtanBtan(A+B)+tanA+tanB-tan(A+B)=0
cosx+cos2x+...+cosnx= [sin(n+1)x+sinnx-sinx]/2sinx
\u8bc1\u660e\uff1a
\u5de6\u8fb9=2sinx(cosx+cos2x+...+cosnx)/2sinx
=[sin2x-0+sin3x-sinx+sin4x-sin2x+...+ sinnx-sin(n-2)x+sin(n+1)x-sin(n-1)x]/2sinx \uff08\u79ef\u5316\u548c\u5dee\uff09
=[sin(n+1)x+sinnx-sinx]/2sinx=\u53f3\u8fb9
\u7b49\u5f0f\u5f97\u8bc1
sinx+sin2x+...+sinnx= - [cos(n+1)x+cosnx-cosx-1]/2sinx
\u8bc1\u660e:
\u5de6\u8fb9=-2sinx[sinx+sin2x+...+sinnx]/(-2sinx)
=[cos2x-cos0+cos3x-cosx+...+cosnx-cos(n-2)x+cos(n+1)x-cos(n-1)x]/(-2sinx)
=- [cos(n+1)x+cosnx-cosx-1]/2sinx=\u53f3\u8fb9
\u7b49\u5f0f\u5f97\u8bc1
\u8bf1\u5bfc\u516c\u5f0f
\u516c\u5f0f\u4e00\uff1a
\u8bbe\u03b1\u4e3a\u4efb\u610f\u89d2\uff0c\u7ec8\u8fb9\u76f8\u540c\u7684\u89d2\u7684\u540c\u4e00\u4e09\u89d2\u51fd\u6570\u7684\u503c\u76f8\u7b49\uff1a
sin\uff082k\u03c0\uff0b\u03b1\uff09\uff1dsin\u03b1
cos\uff082k\u03c0\uff0b\u03b1\uff09\uff1dcos\u03b1
tan\uff082k\u03c0\uff0b\u03b1\uff09\uff1dtan\u03b1
cot\uff082k\u03c0\uff0b\u03b1\uff09\uff1dcot\u03b1
\u516c\u5f0f\u4e8c\uff1a
\u8bbe\u03b1\u4e3a\u4efb\u610f\u89d2\uff0c\u03c0+\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e0e\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a
sin\uff08\u03c0\uff0b\u03b1\uff09\uff1d\uff0dsin\u03b1
cos\uff08\u03c0\uff0b\u03b1\uff09\uff1d\uff0dcos\u03b1
tan\uff08\u03c0\uff0b\u03b1\uff09\uff1dtan\u03b1
cot\uff08\u03c0\uff0b\u03b1\uff09\uff1dcot\u03b1
\u516c\u5f0f\u4e09\uff1a
\u4efb\u610f\u89d2\u03b1\u4e0e -\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a
sin\uff08\uff0d\u03b1\uff09\uff1d\uff0dsin\u03b1
cos\uff08\uff0d\u03b1\uff09\uff1dcos\u03b1
tan\uff08\uff0d\u03b1\uff09\uff1d\uff0dtan\u03b1
cot\uff08\uff0d\u03b1\uff09\uff1d\uff0dcot\u03b1
\u516c\u5f0f\u56db\uff1a
\u5229\u7528\u516c\u5f0f\u4e8c\u548c\u516c\u5f0f\u4e09\u53ef\u4ee5\u5f97\u5230\u03c0-\u03b1\u4e0e\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a
sin\uff08\u03c0\uff0d\u03b1\uff09\uff1dsin\u03b1
cos\uff08\u03c0\uff0d\u03b1\uff09\uff1d\uff0dcos\u03b1
tan\uff08\u03c0\uff0d\u03b1\uff09\uff1d\uff0dtan\u03b1
cot\uff08\u03c0\uff0d\u03b1\uff09\uff1d\uff0dcot\u03b1
\u516c\u5f0f\u4e94\uff1a
\u5229\u7528\u516c\u5f0f\u4e00\u548c\u516c\u5f0f\u4e09\u53ef\u4ee5\u5f97\u52302\u03c0-\u03b1\u4e0e\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a
sin\uff082\u03c0\uff0d\u03b1\uff09\uff1d\uff0dsin\u03b1
cos\uff082\u03c0\uff0d\u03b1\uff09\uff1dcos\u03b1
tan\uff082\u03c0\uff0d\u03b1\uff09\uff1d\uff0dtan\u03b1
cot\uff082\u03c0\uff0d\u03b1\uff09\uff1d\uff0dcot\u03b1
\u516c\u5f0f\u516d\uff1a
\u03c0/2\u00b1\u03b1\u53ca3\u03c0/2\u00b1\u03b1\u4e0e\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a
sin\uff08\u03c0/2\uff0b\u03b1\uff09\uff1dcos\u03b1
cos\uff08\u03c0/2\uff0b\u03b1\uff09\uff1d\uff0dsin\u03b1
tan\uff08\u03c0/2\uff0b\u03b1\uff09\uff1d\uff0dcot\u03b1
cot\uff08\u03c0/2\uff0b\u03b1\uff09\uff1d\uff0dtan\u03b1
sin\uff08\u03c0/2\uff0d\u03b1\uff09\uff1dcos\u03b1
cos\uff08\u03c0/2\uff0d\u03b1\uff09\uff1dsin\u03b1
tan\uff08\u03c0/2\uff0d\u03b1\uff09\uff1dcot\u03b1
cot\uff08\u03c0/2\uff0d\u03b1\uff09\uff1dtan\u03b1
sin\uff083\u03c0/2\uff0b\u03b1\uff09\uff1d\uff0dcos\u03b1
cos\uff083\u03c0/2\uff0b\u03b1\uff09\uff1dsin\u03b1
tan\uff083\u03c0/2\uff0b\u03b1\uff09\uff1d\uff0dcot\u03b1
cot\uff083\u03c0/2\uff0b\u03b1\uff09\uff1d\uff0dtan\u03b1
sin\uff083\u03c0/2\uff0d\u03b1\uff09\uff1d\uff0dcos\u03b1
cos\uff083\u03c0/2\uff0d\u03b1\uff09\uff1d\uff0dsin\u03b1
tan\uff083\u03c0/2\uff0d\u03b1\uff09\uff1dcot\u03b1
cot\uff083\u03c0/2\uff0d\u03b1\uff09\uff1dtan\u03b1
(\u4ee5\u4e0ak\u2208Z)
\u6b63\u5f26\u5b9a\u7406\u662f\u6307\u5728\u4e09\u89d2\u5f62\u4e2d\uff0c\u5404\u8fb9\u548c\u5b83\u6240\u5bf9\u7684\u89d2\u7684\u6b63\u5f26\u7684\u6bd4\u76f8\u7b49\uff0c\u5373a/sinA=b/sinB=c/sinC=2R \uff0e(\u5176\u4e2dR\u4e3a\u5916\u63a5\u5706\u7684\u534a\u5f84)
\u4f59\u5f26\u5b9a\u7406\u662f\u6307\u4e09\u89d2\u5f62\u4e2d\u4efb\u4f55\u4e00\u8fb9\u7684\u5e73\u65b9\u7b49\u4e8e\u5176\u5b83\u4e24\u8fb9\u7684\u5e73\u65b9\u548c\u51cf\u53bb\u8fd9\u4e24\u8fb9\u4e0e\u5b83\u4eec\u5939\u89d2\u7684\u4f59\u5f26\u7684\u79ef\u76842\u500d\uff0c\u5373a^2=b^2+c^2-2bc cosA
\u89d2A\u7684\u5bf9\u8fb9\u4e8e\u659c\u8fb9\u7684\u6bd4\u53eb\u505a\u89d2A\u7684\u6b63\u5f26\uff0c\u8bb0\u4f5csinA\uff0c\u5373sinA=\u89d2A\u7684\u5bf9\u8fb9/\u659c\u8fb9
\u659c\u8fb9\u4e0e\u90bb\u8fb9\u5939\u89d2a
sin=y/r
\u65e0\u8bbay>x\u6216y\u2264x
\u65e0\u8bbaa\u591a\u5927\u591a\u5c0f\u53ef\u4ee5\u4efb\u610f\u5927\u5c0f
\u6b63\u5f26\u7684\u6700\u5927\u503c\u4e3a1 \u6700\u5c0f\u503c\u4e3a-1
\u4e09\u89d2\u6052\u7b49\u5f0f
\u5bf9\u4e8e\u4efb\u610f\u975e\u76f4\u89d2\u4e09\u89d2\u5f62\u4e2d,\u5982\u4e09\u89d2\u5f62ABC,\u603b\u6709tanA+tanB+tanC=tanAtanBtanC
\u8bc1\u660e:
\u5df2\u77e5(A+B)=(\u03c0-C)
\u6240\u4ee5tan(A+B)=tan(\u03c0-C)
\u5219(tanA+tanB)/(1-tanAtanB)=(tan\u03c0-tanC)/(1+tan\u03c0tanC)
\u6574\u7406\u53ef\u5f97
tanA+tanB+tanC=tanAtanBtanC
\u7c7b\u4f3c\u5730,\u6211\u4eec\u540c\u6837\u4e5f\u53ef\u4ee5\u6c42\u8bc1:\u5f53\u03b1+\u03b2+\u03b3=n\u03c0(n\u2208Z)\u65f6\uff0c\u603b\u6709tan\u03b1+tan\u03b2+tan\u03b3=tan\u03b1tan\u03b2tan\u03b3
\u5411\u91cf\u8ba1\u7b97
\u8bbea=\uff08x\uff0cy\uff09\uff0cb=(x'\uff0cy')\u3002
1\u3001\u5411\u91cf\u7684\u52a0\u6cd5
\u5411\u91cf\u7684\u52a0\u6cd5\u6ee1\u8db3\u5e73\u884c\u56db\u8fb9\u5f62\u6cd5\u5219\u548c\u4e09\u89d2\u5f62\u6cd5\u5219\u3002
AB+BC=AC\u3002
a+b=(x+x'\uff0cy+y')\u3002
a+0=0+a=a\u3002
\u5411\u91cf\u52a0\u6cd5\u7684\u8fd0\u7b97\u5f8b\uff1a
\u4ea4\u6362\u5f8b\uff1aa+b=b+a\uff1b
\u7ed3\u5408\u5f8b\uff1a(a+b)+c=a+(b+c)\u3002
2\u3001\u5411\u91cf\u7684\u51cf\u6cd5
\u5982\u679ca\u3001b\u662f\u4e92\u4e3a\u76f8\u53cd\u7684\u5411\u91cf\uff0c\u90a3\u4e48a=-b\uff0cb=-a\uff0ca+b=0. 0\u7684\u53cd\u5411\u91cf\u4e3a0
AB-AC=CB. \u5373\u201c\u5171\u540c\u8d77\u70b9\uff0c\u6307\u5411\u88ab\u51cf\u201d
a=(x,y) b=(x',y') \u5219 a-b=(x-x',y-y').
4\u3001\u6570\u4e58\u5411\u91cf
\u5b9e\u6570\u03bb\u548c\u5411\u91cfa\u7684\u4e58\u79ef\u662f\u4e00\u4e2a\u5411\u91cf\uff0c\u8bb0\u4f5c\u03bba\uff0c\u4e14\u2223\u03bba\u2223=\u2223\u03bb\u2223\u00b7\u2223a\u2223\u3002
\u5f53\u03bb\uff1e0\u65f6\uff0c\u03bba\u4e0ea\u540c\u65b9\u5411\uff1b
\u5f53\u03bb\uff1c0\u65f6\uff0c\u03bba\u4e0ea\u53cd\u65b9\u5411\uff1b
\u5f53\u03bb=0\u65f6\uff0c\u03bba=0\uff0c\u65b9\u5411\u4efb\u610f\u3002
\u5f53a=0\u65f6\uff0c\u5bf9\u4e8e\u4efb\u610f\u5b9e\u6570\u03bb\uff0c\u90fd\u6709\u03bba=0\u3002
\u6ce8\uff1a\u6309\u5b9a\u4e49\u77e5\uff0c\u5982\u679c\u03bba=0\uff0c\u90a3\u4e48\u03bb=0\u6216a=0\u3002
\u5b9e\u6570\u03bb\u53eb\u505a\u5411\u91cfa\u7684\u7cfb\u6570\uff0c\u4e58\u6570\u5411\u91cf\u03bba\u7684\u51e0\u4f55\u610f\u4e49\u5c31\u662f\u5c06\u8868\u793a\u5411\u91cfa\u7684\u6709\u5411\u7ebf\u6bb5\u4f38\u957f\u6216\u538b\u7f29\u3002
\u5f53\u2223\u03bb\u2223\uff1e1\u65f6\uff0c\u8868\u793a\u5411\u91cfa\u7684\u6709\u5411\u7ebf\u6bb5\u5728\u539f\u65b9\u5411\uff08\u03bb\uff1e0\uff09\u6216\u53cd\u65b9\u5411\uff08\u03bb\uff1c0\uff09\u4e0a\u4f38\u957f\u4e3a\u539f\u6765\u7684\u2223\u03bb\u2223\u500d\uff1b
\u5f53\u2223\u03bb\u2223\uff1c1\u65f6\uff0c\u8868\u793a\u5411\u91cfa\u7684\u6709\u5411\u7ebf\u6bb5\u5728\u539f\u65b9\u5411\uff08\u03bb\uff1e0\uff09\u6216\u53cd\u65b9\u5411\uff08\u03bb\uff1c0\uff09\u4e0a\u7f29\u77ed\u4e3a\u539f\u6765\u7684\u2223\u03bb\u2223\u500d\u3002
\u6570\u4e0e\u5411\u91cf\u7684\u4e58\u6cd5\u6ee1\u8db3\u4e0b\u9762\u7684\u8fd0\u7b97\u5f8b
\u7ed3\u5408\u5f8b\uff1a(\u03bba)\u00b7b=\u03bb(a\u00b7b)=(a\u00b7\u03bbb)\u3002
\u5411\u91cf\u5bf9\u4e8e\u6570\u7684\u5206\u914d\u5f8b\uff08\u7b2c\u4e00\u5206\u914d\u5f8b\uff09\uff1a(\u03bb+\u03bc)a=\u03bba+\u03bca.
\u6570\u5bf9\u4e8e\u5411\u91cf\u7684\u5206\u914d\u5f8b\uff08\u7b2c\u4e8c\u5206\u914d\u5f8b\uff09\uff1a\u03bb(a+b)=\u03bba+\u03bbb.
\u6570\u4e58\u5411\u91cf\u7684\u6d88\u53bb\u5f8b\uff1a\u2460 \u5982\u679c\u5b9e\u6570\u03bb\u22600\u4e14\u03bba=\u03bbb\uff0c\u90a3\u4e48a=b\u3002\u2461 \u5982\u679ca\u22600\u4e14\u03bba=\u03bca\uff0c\u90a3\u4e48\u03bb=\u03bc\u3002
3\u3001\u5411\u91cf\u7684\u7684\u6570\u91cf\u79ef
\u5b9a\u4e49\uff1a\u4e24\u4e2a\u975e\u96f6\u5411\u91cf\u7684\u5939\u89d2\u8bb0\u4e3a\u3008a\uff0cb\u3009\uff0c\u4e14\u3008a\uff0cb\u3009\u2208[0\uff0c\u03c0]\u3002
\u5b9a\u4e49\uff1a\u4e24\u4e2a\u5411\u91cf\u7684\u6570\u91cf\u79ef\uff08\u5185\u79ef\u3001\u70b9\u79ef\uff09\u662f\u4e00\u4e2a\u6570\u91cf\uff0c\u8bb0\u4f5ca\u00b7b\u3002\u82e5a\u3001b\u4e0d\u5171\u7ebf\uff0c\u5219a\u00b7b=|a|\u00b7|b|\u00b7cos\u3008a\uff0cb\u3009\uff1b\u82e5a\u3001b\u5171\u7ebf\uff0c\u5219a\u00b7b=+-\u2223a\u2223\u2223b\u2223\u3002
\u5411\u91cf\u7684\u6570\u91cf\u79ef\u7684\u5750\u6807\u8868\u793a\uff1aa\u00b7b=x\u00b7x'+y\u00b7y'\u3002
\u5411\u91cf\u7684\u6570\u91cf\u79ef\u7684\u8fd0\u7b97\u7387
a\u00b7b=b\u00b7a\uff08\u4ea4\u6362\u7387\uff09\uff1b
\uff08a+b)\u00b7c=a\u00b7c+b\u00b7c\uff08\u5206\u914d\u7387\uff09\uff1b
\u5411\u91cf\u7684\u6570\u91cf\u79ef\u7684\u6027\u8d28
a\u00b7a=|a|\u7684\u5e73\u65b9\u3002
a\u22a5b \u3008=\u3009a\u00b7b=0\u3002
|a\u00b7b|\u2264|a|\u00b7|b|\u3002
\u5411\u91cf\u7684\u6570\u91cf\u79ef\u4e0e\u5b9e\u6570\u8fd0\u7b97\u7684\u4e3b\u8981\u4e0d\u540c\u70b9
1\u3001\u5411\u91cf\u7684\u6570\u91cf\u79ef\u4e0d\u6ee1\u8db3\u7ed3\u5408\u5f8b\uff0c\u5373\uff1a(a\u00b7b)\u00b7c\u2260a\u00b7(b\u00b7c)\uff1b\u4f8b\u5982\uff1a(a\u00b7b)^2\u2260a^2\u00b7b^2\u3002
2\u3001\u5411\u91cf\u7684\u6570\u91cf\u79ef\u4e0d\u6ee1\u8db3\u6d88\u53bb\u5f8b\uff0c\u5373\uff1a\u7531 a\u00b7b=a\u00b7c (a\u22600)\uff0c\u63a8\u4e0d\u51fa b=c\u3002
3\u3001|a\u00b7b|\u2260|a|\u00b7|b|
4\u3001\u7531 |a|=|b| \uff0c\u63a8\u4e0d\u51fa a=b\u6216a=-b\u3002
\u7acb\u4f53\u51e0\u4f55\u57fa\u672c\u8bfe\u9898
\u5305\u62ec:
- \u9762\u548c\u7ebf\u7684\u91cd\u5408
- \u4e24\u9762\u89d2\u548c\u7acb\u4f53\u89d2
- \u65b9\u5757, \u957f\u65b9\u4f53, \u5e73\u884c\u516d\u9762\u4f53
- \u56db\u9762\u4f53\u548c\u5176\u4ed6\u68f1\u9525
- \u68f1\u67f1
- \u516b\u9762\u4f53, \u5341\u4e8c\u9762\u4f53, \u4e8c\u5341\u9762\u4f53
- \u5706\u9525\uff0c\u5706\u67f1
- \u7403
- \u5176\u4ed6\u4e8c\u6b21\u66f2\u9762: \u56de\u8f6c\u692d\u7403, \u692d\u7403, \u629b\u7269\u9762 \uff0c\u53cc\u66f2\u9762
\u516c\u7406
\u7acb\u4f53\u51e0\u4f55\u4e2d\u67094\u4e2a\u516c\u7406
\u516c\u74061 \u5982\u679c\u4e00\u6761\u76f4\u7ebf\u4e0a\u7684\u4e24\u70b9\u5728\u4e00\u4e2a\u5e73\u9762\u5185\uff0c\u90a3\u4e48\u8fd9\u6761\u76f4\u7ebf\u5728\u6b64\u5e73\u9762\u5185\uff0e
\u516c\u74062 \u8fc7\u4e0d\u5728\u4e00\u6761\u76f4\u7ebf\u4e0a\u7684\u4e09\u70b9\uff0c\u6709\u4e14\u53ea\u6709\u4e00\u4e2a\u5e73\u9762\uff0e
\u516c\u74063 \u5982\u679c\u4e24\u4e2a\u4e0d\u91cd\u5408\u7684\u5e73\u9762\u6709\u4e00\u4e2a\u516c\u5171\u70b9\uff0c\u90a3\u4e48\u5b83\u4eec\u6709\u4e14\u53ea\u6709\u4e00\u6761\u8fc7\u8be5\u70b9\u7684\u516c\u5171\u76f4\u7ebf\uff0e
\u516c\u74064 \u5e73\u884c\u4e8e\u540c\u4e00\u6761\u76f4\u7ebf\u7684\u4e24\u6761\u76f4\u7ebf\u5e73\u884c\uff0e
\u7acb\u65b9\u56fe\u5f62
\u7acb\u4f53\u51e0\u4f55\u516c\u5f0f
\u540d\u79f0 \u7b26\u53f7 \u9762\u79efS \u4f53\u79efV
\u6b63\u65b9\u4f53 a\u2014\u2014\u8fb9\u957f S\uff1d6a\uff3e2 V\uff1da\uff3e3
\u957f\u65b9\u4f53 a\u2014\u2014\u957f S\uff1d2(ab+ac+bc) V\uff1dabc
b\u2014\u2014\u5bbd
c\u2014\u2014\u9ad8
\u68f1\u67f1 S\u2014\u2014\u5e95\u9762\u79ef V\uff1dSh
h\u2014\u2014\u9ad8
\u68f1\u9525 S\u2014\u2014\u5e95\u9762\u79ef V\uff1dSh\uff0f3
h\u2014\u2014\u9ad8
\u68f1\u53f0 S1\u548cS2\u2014\u2014\u4e0a\u3001\u4e0b\u5e95\u9762\u79ef V\uff1dh\u3014S1\uff0bS2\uff0b\u221a\uff08S1\uff3e2\uff09\uff0f2\u3015\uff0f3
h\u2014\u2014\u9ad8
\u62df\u67f1\u4f53 S1\u2014\u2014\u4e0a\u5e95\u9762\u79ef V\uff1dh\uff08S1\uff0bS2\uff0b4S0\uff09\uff0f6
S2\u2014\u2014\u4e0b\u5e95\u9762\u79ef
S0\u2014\u2014\u4e2d\u622a\u9762\u79ef
h\u2014\u2014\u9ad8
\u5706\u67f1 r\u2014\u2014\u5e95\u534a\u5f84 C\uff1d2\u03c0r V\uff1dS\u5e95h=\u220frh
h\u2014\u2014\u9ad8
C\u2014\u2014\u5e95\u9762\u5468\u957f
S\u5e95\u2014\u2014\u5e95\u9762\u79ef S\u5e95\uff1d\u03c0R\uff3e2
S\u4fa7\u2014\u2014\u4fa7\u9762\u79ef S\u4fa7\uff1dCh
S\u8868\u2014\u2014\u8868\u9762\u79ef S\u8868\uff1dCh\uff0b2S\u5e95
S\u5e95\uff1d\u03c0r\uff3e2
\u7a7a\u5fc3\u5706\u67f1 R\u2014\u2014\u5916\u5706\u534a\u5f84
r\u2014\u2014\u5185\u5706\u534a\u5f84
h\u2014\u2014\u9ad8 V\uff1d\u03c0h(R\uff3e2-r\uff3e2)
\u76f4\u5706\u9525 r\u2014\u2014\u5e95\u534a\u5f84
h\u2014\u2014\u9ad8 V\uff1d\u03c0r\uff3e2h/3
\u5706\u53f0 r\u2014\u2014\u4e0a\u5e95\u534a\u5f84
R\u2014\u2014\u4e0b\u5e95\u534a\u5f84
h\u2014\u2014\u9ad8 V\uff1d\u03c0h(R\uff3e2\uff0bRr\uff0br\uff3e2)/3
\u7403 r\u2014\u2014\u534a\u5f84
d\u2014\u2014\u76f4\u5f84 V\uff1d4/3\u03c0r\uff3e3\uff1d\u03c0d\uff3e2/6
\u7403\u7f3a h\u2014\u2014\u7403\u7f3a\u9ad8
r\u2014\u2014\u7403\u534a\u5f84
a\u2014\u2014\u7403\u7f3a\u5e95\u534a\u5f84 a\uff3e2\uff1dh(2r-h) V\uff1d\u03c0h(3a\uff3e2+h\uff3e2)/6 \uff1d\u03c0h2(3r-h)/3
\u7403\u53f0 r1\u548cr2\u2014\u2014\u7403\u53f0\u4e0a\u3001\u4e0b\u5e95\u534a\u5f84
h\u2014\u2014\u9ad8 V\uff1d\u03c0h[3(r12\uff0br22)+h2]/6
\u5706\u73af\u4f53 R\u2014\u2014\u73af\u4f53\u534a\u5f84
D\u2014\u2014\u73af\u4f53\u76f4\u5f84
r\u2014\u2014\u73af\u4f53\u622a\u9762\u534a\u5f84
d\u2014\u2014\u73af\u4f53\u622a\u9762\u76f4\u5f84 V\uff1d2\u03c0\uff3e2Rr\uff3e2 \uff1d\u03c0\uff3e2Dd\uff3e2/4
\u6876\u72b6\u4f53 D\u2014\u2014\u6876\u8179\u76f4\u5f84
d\u2014\u2014\u6876\u5e95\u76f4\u5f84
h\u2014\u2014\u6876\u9ad8 V\uff1d\u03c0h(2D\uff3e2\uff0bd2\uff3e)/12 (\u6bcd\u7ebf\u662f\u5706\u5f27\u5f62,\u5706\u5fc3\u662f\u6876\u7684\u4e2d\u5fc3)
V\uff1d\u03c0h(2D\uff3e2\uff0bDd\uff0b3d\uff3e2/4)/15 (\u6bcd\u7ebf\u662f\u629b\u7269\u7ebf\u5f62)
\u5e73\u9762\u89e3\u6790\u51e0\u4f55\u5305\u542b\u4e00\u4e0b\u51e0\u90e8\u5206
\u4e00 \u76f4\u89d2\u5750\u6807
1.1 \u6709\u5411\u7ebf\u6bb5
1.2 \u76f4\u7ebf\u4e0a\u7684\u70b9\u7684\u76f4\u89d2\u5750\u6807
1.3 \u51e0\u4e2a\u57fa\u672c\u516c\u5f0f
1.4 \u5e73\u9762\u4e0a\u7684\u70b9\u7684\u76f4\u89d2\u5750\u6807
1.5 \u5c04\u5f71\u7684\u57fa\u672c\u539f\u7406
1.6 \u51e0\u4e2a\u57fa\u672c\u516c\u5f0f
\u4e8c \u66f2\u7ebf\u4e0e\u8bae\u7a0b
2.1 \u66f2\u7ebf\u7684\u76f4\u89e3\u5750\u6807\u65b9\u7a0b\u7684\u5b9a\u4e49
2.2 \u5df2\u5404\u66f2\u7ebf\uff0c\u6c42\u5b83\u7684\u65b9\u7a0b
2.3 \u5df2\u77e5\u66f2\u7ebf\u7684\u65b9\u7a0b\uff0c\u63cf\u7ed8\u66f2\u7ebf
2.4 \u66f2\u7ebf\u7684\u4ea4\u70b9
\u4e09 \u76f4\u7ebf
3.1 \u76f4\u7ebf\u7684\u503e\u659c\u89d2\u548c\u659c\u7387
3.2 \u76f4\u7ebf\u7684\u65b9\u7a0b
Y=kx+b
3.3 \u76f4\u7ebf\u5230\u70b9\u7684\u6709\u5411\u8ddd\u79bb
3.4 \u4e8c\u5143\u4e00\u6b21\u4e0d\u7b49\u5f0f\u8868\u793a\u7684\u5e73\u9762\u533a\u57df
3.5 \u4e24\u6761\u76f4\u7ebf\u7684\u76f8\u5173\u4f4d\u7f6e
3.6 \u4e8c\u5143\u4e8c\u65b9\u7a0b\u8868\u793a\u4e24\u6761\u76f4\u7ebf\u7684\u6761\u4ef6
3.7 \u4e09\u6761\u76f4\u7ebf\u7684\u76f8\u5173\u4f4d\u7f6e
3.8 \u76f4\u7ebf\u7cfb
\u56db \u5706
4.1 \u5706\u7684\u5b9a\u4e49
4.2 \u5706\u7684\u65b9\u7a0b
4.3 \u70b9\u548c\u5706\u7684\u76f8\u5173\u4f4d\u7f6e
4.4 \u5706\u7684\u5207\u7ebf
4.5 \u70b9\u5173\u4e8e\u5706\u7684\u5207\u70b9\u5f26\u4e0e\u6781\u7ebf
4.6 \u5171\u8f74\u5706\u7cfb
4.7 \u5e73\u9762\u4e0a\u7684\u53cd\u6f14\u53d8\u6362
\u4e94 \u692d\u5706
5.1 \u692d\u5706\u7684\u5b9a\u4e49
5.2 \u7528\u5e73\u9762\u622a\u76f4\u5706\u9525\u9762\u53ef\u4ee5\u5f97\u5230\u692d\u5706
5.3 \u692d\u5706\u7684\u6807\u51c6\u65b9\u7a0b
5.4 \u692d\u5706\u7684\u57fa\u672c\u6027\u8d28\u53ca\u6709\u5173\u6982\u5ff5
5.5 \u70b9\u548c\u692d\u5706\u7684\u76f8\u5173\u4f4d\u7f6e
5.6 \u692d\u5706\u7684\u5207\u7ebf\u4e0e\u6cd5\u7ebf
5.7 \u70b9\u5173\u4e8e\u692d\u5706\u7684\u5207\u70b9\u5f26\u4e0e\u6781\u7ebf
5.8 \u692d\u5706\u7684\u9762\u79ef
\u516d \u53cc\u66f2\u7ebf
6.1 \u53cc\u66f2\u7ebf\u7684\u5b9a\u4e49
6.2 \u7528\u5e73\u9762\u622a\u76f4\u5706\u9525\u9762\u53ef\u4ee5\u5f97\u5230\u53cc\u66f2\u7ebf
6.3 \u53cc\u66f2\u7ebf\u7684\u6807\u51c6\u65b9\u7a0b
6.4 \u53cc\u66f2\u7ebf\u7684\u57fa\u672c\u6027\u8d28\u53ca\u6709\u5173\u6982\u5ff5
6.5 \u7b49\u8f74\u53cc\u66f2\u7ebf
6.6 \u5171\u8f6d\u53cc\u66f2\u7ebf
6.7 \u70b9\u548c\u53cc\u66f2\u7ebf\u7684\u76f8\u5173\u4f4d\u7f6e
6.8 \u53cc\u66f2\u7ebf\u7684\u5207\u7ebf\u4e0e\u6cd5\u7ebf
6.9 \u70b9\u5173\u4e8e\u53cc\u66f2\u7ebf\u7684\u5207\u70b9\u5f26\u4e0e\u6781\u7ebf
\u4e03 \u629b\u7269\u7ebf
7.1 \u629b\u7269\u7ebf\u7684\u5b9a\u4e49
7.2 \u7528\u5e73\u9762\u622a\u76f4\u5706\u9525\u9762\u53ef\u4ee5\u5f97\u5230\u629b\u7269\u7ebf
7.3 \u629b\u7269\u7ebf\u7684\u6807\u51c6\u65b9\u7a0b
7.4 \u629b\u7269\u7ebf\u7684\u57fa\u672c\u6027\u8d28\u53ca\u6709\u5173\u6982\u5ff5
7.5 \u70b9\u548c\u629b\u7269\u7ebf\u7684\u76f8\u5173\u4f4d\u7f6e
7.6 \u629b\u7269\u7ebf\u7684\u5207\u7ebf\u4e0e\u6cd5\u7ebf
7.7 \u70b9\u5173\u4e8e\u629b\u7269\u7ebf\u7684\u5207\u70b9\u5f26\u4e0e\u6781\u7ebf
7.8 \u629b\u7269\u7ebf\u5f13\u5f62\u7684\u9762\u79ef
\u516b \u5750\u6807\u53d8\u6362\u00b7\u4e8c\u6b21\u66f2\u7ebf\u7684\u4e00\u822c\u7406\u8bba
8.1 \u5750\u6807\u53d8\u6362\u7684\u6982\u5ff5
8.2 \u5750\u6807\u8f74\u7684\u5e73\u79fb
8.3 \u5229\u7528\u5e73\u79fb\u5316\u7b80\u66f2\u7ebf\u65b9\u7a0b
8.4 \u5706\u9525\u66f2\u7ebf\u7684\u66f4\u4e00\u822c\u7684\u6807\u51c6\u65b9\u7a0b
8.5 \u5750\u6807\u8f74\u7684\u65cb\u8f6c
8.6 \u5750\u6807\u53d8\u6362\u7684\u4e00\u822c\u516c\u5f0f
8.7 \u66f2\u7ebf\u7684\u5206\u7c7b
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8.9 \u4e8c\u5143\u4e8c\u6b21\u65b9\u7a0b\u7684\u66f2\u7ebf
8.10 \u4e8c\u6b21\u66f2\u7ebf\u65b9\u7a0b\u7684\u5316\u7b80
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\u4e09 \u6570\u5217
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sin(A+B)=sinAcosB+cosAsinB
sin(A-B)=sinAcosB-sinBcosA
cos(A+B)=cosAcosB-sinAsinB
cos(A-B)=cosAcosB+sinAsinB
tan(A+B)=(tanA+tanB)/(1-tanAtanB)
tan(A-B)=(tanA-tanB)/(1+tanAtanB)
二）用以上公式可推出下列二倍角公式
tan2A=2tanA/[1-(tanA)^2]
cos2a=(cosa)^2-(sina)^2=2(cosa)^2 -1=1-2(sina)^2
（上面这个余弦的很重要）
sin2A=2sinA*cosA
三）半角的只需记住这个：
tan(A/2)=(1-cosA)/sinA=sinA/(1+cosA)
四）用二倍角中的余弦可推出降幂公式
(sinA)^2=(1-cos2A)/2
(cosA)^2=(1+cos2A)/2
五）用以上降幂公式可推出以下常用的化简公式
1-cosA=sin^(A/2)*2
1-sinA=cos^(A/2)*2
万能公式
令tan(a/2)=t
sina=2t/(1+t^2)
cosa=(1-t^2)/(1+t^2)
tana=2t/(1-t^2)
二次三项式因式分解公式：x^2+(p+q)x+pq=(x+p)(x+q)
立方差 a³-b³=(a-b)(a²+ab+b²)
立方和 a³+b³=(a+b)(a²-ab+b²)
完全平方和公式
(a+b)^2=a^2+2ab+b^2
完全平方差公式
(a-b)^2=a^2-2ab+b^2
完全立方和公式
(a+b)3=(a+b)(a+b)(a+b)=(a2+2ab+b2)(a+b)=a3+3a2b+3ab2+b3
完全立方差公式
(a-b)3=(a-b)(a-b)(a-b)=(a2-2ab+b2)(a-b)=a3-3a2b+3ab2-b3
绛旓細涓锛変袱瑙掑拰宸叕寮 锛堝啓鐨勯兘瑕佽锛塻in(A+B)=sinAcosB+cosAsinB sin(A-B)=sinAcosB-sinBcosA cos(A+B)=cosAcosB-sinAsinB cos(A-B)=cosAcosB+sinAsinB tan(A+B)=(tanA+tanB)/(1-tanAtanB)tan(A-B)=(tanA-tanB)/(1+tanAtanB)浜岋級鐢ㄤ互涓婂叕寮忓彲鎺ㄥ嚭涓嬪垪浜屽嶈鍏紡 tan2A=2...
绛旓細鍊嶈鍏紡 tan2A=2tanA/(1-tan2A) ctg2A=(ctg2A-1)/2ctga cos2a=cos2a-sin2a=2cos2a-1=1-2sin2a 鍗婅鍏紡 sin(A/2)=鈭((1-cosA)/2) sin(A/2)=-鈭((1-cosA)/2) cos(A/2)=鈭((1+cosA)/2) cos(A/2)=-鈭((1+cosA)/2) tan(A/2)=鈭((1-cosA)/((1+cosA)) ...
绛旓細tan(伪-尾)=(tan伪-tan尾)/(1+tan伪路tan尾)路杈呭姪瑙掑叕寮忥細Asin伪+Bcos伪=(A^2+B^2)^(1/2)sin(伪+t)锛屽叾涓 sint=B/(A^2+B^2)^(1/2)cost=A/(A^2+B^2)^(1/2)路鍊嶈鍏紡锛歴in(2伪)=2sin伪路cos伪=2/(tan伪+cot伪)cos(2伪)=cos^2(伪)-sin^2(伪)=2cos^2(...
绛旓細tan(A/2)=鈭((1-cosA)/((1+cosA)) tan(A/2)=-鈭((1-cosA)/((1+cosA))cot(A/2)=鈭((1+cosA)/((1-cosA)) cot(A/2)=-鈭((1+cosA)/((1-cosA))鍊嶈鍏紡 tan2A=2tanA/(1-tan2A) cot2A=(cot2A-1)/2cota cos2a=cos2a-sin2a=2cos2a-1=1-2sin2a 鈥2涓哄钩鏂 sin...
绛旓細璺眰楂樹竴浜烘暀鐗堟暟瀛蹇呬慨涓銆蹇呬慨浜鐨勫畬鏁村叕寮忓ぇ鍏!!! 蹇呬慨浜屾垜瑕佺洿绾夸笌鏂圭▼,鍦嗕笌鏂圭▼鐨勫叕寮忓ぇ鍏,鎴戣繕瑕蹇呬慨涓鐨闆嗗悎,鍑芥暟鐨勫叕寮,鏈濂借繕缁欐垜涓浜涘父鑰冮鐨勮В棰樻濊矾缁,灏忓紵浼氭劅婵涓嶅敖鐨!!!... 蹇呬慨浜屾垜瑕佺洿绾夸笌鏂圭▼,鍦嗕笌鏂圭▼鐨勫叕寮忓ぇ鍏,鎴戣繕瑕佸繀淇竴鐨勯泦鍚,鍑芥暟鐨勫叕寮,鏈濂借繕缁欐垜涓浜涘父鑰冮鐨勮В棰樻濊矾缁,灏忓紵...
绛旓細楂樹竴鏁板蹇呬慨涓鎵鏈鍏紡褰掔撼鏄涓嬶細1銆侀攼瑙掍笁瑙掑嚱鏁板叕寮忥細sin伪=鈭犖辩殑瀵硅竟/鏂滆竟銆2銆佷笁鍊嶈鍏紡锛歴in3伪=4sin伪路sin(蟺/3+伪)sin(蟺/3-伪)銆3銆佽緟鍔╄鍏紡锛欰sin伪+Bcos伪=(A^2+B^2)^(1/2)sin(伪+t)銆4銆侀檷骞傚叕寮忥細sin^2(伪)=(1-cos(2伪))/2=versin(2伪)/2銆5銆佹帹瀵...
绛旓細n+1)=n(n+1)(n+2)/3 3銆佹寮﹀畾鐞 a/sinA=b/sinB=c/sinC=2R 娉細 鍏朵腑 R 琛ㄧず涓夎褰㈢殑澶栨帴鍦嗗崐寰 4銆佷綑寮﹀畾鐞 b2=a2+c2-2accosB 娉細瑙払鏄竟a鍜岃竟c鐨勫す瑙 5銆併愬嶈鍏紡銆憈an2A=2tanA/(1-tan2A) ctg2A=(ctg2A-1)/2ctga cos2a=cos2a-sin2a=2cos2a-1=1-2sin2a ...
绛旓細涓锛変袱瑙掑拰宸叕寮 锛堝啓鐨勯兘瑕佽锛塻in(A+B)=sinAcosB+cosAsinB sin(A-B)=sinAcosB-sinBcosA �cos(A+B)=cosAcosB-sinAsinB cos(A-B)=cosAcosB+sinAsinB tan(A+B)=(tanA+tanB)/(1-tanAtanB)tan(A-B)=(tanA-tanB)/(1+tanAtanB)浜岋級鐢ㄤ互涓婂叕寮忓彲鎺ㄥ嚭涓嬪垪浜屽嶈鍏紡 tan2A=...
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