cos2x-sin2x=? Cos2x等于什么？
cos2x+sin2x=\uff1f \u600e\u4e48\u7b97\uff1f \u8be6\u7ec6\u8fc7\u7a0b\uff0c\u8fd8\u6709\u7c7b\u4f3c\u8fd9\u79cd\u9898\u7684\u89e3\u6cd5cos2x+sin2x=\u221a2\uff08\u221a2/2*cos2x+\u221a2/2*sin2x\uff09=\u221a2(cos(pi/4)cos2x+sin(pi/4)sin2x)=\u221a2 cos(2x-pi/4)\u6216\u8005=\u221a2(sin(pi/4)cos2x+cos(pi/4)sin2x)=\u221a2sin(2x+pi/4)\uff0cpi\u5c31\u662f\u03c0\u3002
\u8fd9\u7c7b\u578b\u7684\u9898\u76ee\u53ef\u4ee5\u8fd0\u7528\u548c\u5dee\u516c\u5f0f\u6765\u6c42\uff1a
1\u3001sin ( \u03b1 \u00b1 \u03b2 ) = sin\u03b1 \u00b7 cos\u03b2 \u00b1 cos\u03b1 \u00b7 sin\u03b2
2\u3001sin ( \u03b1 + \u03b2 + \u03b3 ) = sin\u03b1 \u00b7 cos\u03b2 \u00b7 cos\u03b3 + cos\u03b1 \u00b7 sin\u03b2 \u00b7 cos\u03b3 + cos\u03b1 \u00b7 cos\u03b2 \u00b7 sin\u03b3 - sin\u03b1 \u00b7 sin\u03b2 \u00b7 sin\u03b3
3\u3001cos ( \u03b1 \u00b1 \u03b2 ) = cos\u03b1 cos\u03b2 ∓ sin\u03b2 sin\u03b1
4\u3001tan ( \u03b1 \u00b1 \u03b2 ) = ( tan\u03b1 \u00b1 tan\u03b2 ) / ( 1 ∓ tan\u03b1 tan\u03b2 )
\u6269\u5c55\u8d44\u6599\uff1a
\u9996\u5148\uff0c\u662f\u4efb\u610f\u89d2\uff0c\u5c31\u662f\u4e00\u4e9b\u89d2\u7684\u8f6c\u5316\uff0c\u8fd8\u6709\u8ba1\u7b97\u6247\u5f62\u7684\u9762\u79ef\uff0c\u6bd4\u8f83\u5e38\u8003\u7684\u662f\u4e09\u89d2\u51fd\u6570\uff0c\u5176\u4e2d\u500d\u89d2\u516c\u5f0f\u6bd4\u8f83\u5e38\u89c1\uff0c\u8fd8\u6709\u4e0a\u9762\u90a3\u79cd\u9898\u3002
\u4e09\u89d2\u51fd\u6570\u5982\u679c\u4f60\u61c2\u5f97\u79ef\u5316\u548c\u5dee\uff08\u548c\u5dee\u5316\u79ef\uff09\u7684\u8bdd\u8fd9\u4e9b\u5c31\u5f88\u7b80\u5355\uff08\u4e0d\u77e5\u9053\u4f60\u4eec\u73b0\u5728\u6709\u6ca1\u6709\u8981\u6c42\uff09\uff0ccosa*cosb=1/2*[cos(a+b)+cos(a-b)]; sina*sinb=1/2[cos(a-b)-cos(a+b)],\u5176\u4ed6\u7684\u53ef\u4ee5\u7c7b\u63a8\u51fa\u6765\u3002\u8fd8\u6709\u5c31\u662f\u5982\u679c\u5206\u5b50\u5206\u6bcd\u6b63\u5f26\u548c\u4f59\u5f26\u7684\u5e42\u6b21\u662f\u4e00\u6837\u7684\u8bdd\u3002\u5982\uff08cosa+sina\uff09/(3cosa-2sina)\uff0c\u8fd9\u79cd\u9898\u5c31\u559c\u6b22\u5316\u6210\u6b63\u5207\uff08tana\u4e00\u822c\u4f1a\u7ed9\u51fa\uff09\u6765\u7b97\uff0c\u5982\u4e0a\u4e0b\u90fd\u9664\u4ee5cosa\u6216\u8005sina\u3002
\u53c2\u8003\u8d44\u6599\uff1a\u767e\u5ea6\u767e\u79d1\u2014\u2014\u6b63\u5f26
\u4e09\u89d2\u51fd\u6570\u4ee3\u6362\uff1a
cos2X=(cosX)^2-(sinX)^2=2*(cosX)^2-1=1-2*(sinX)^2
\u5373\uff1acos2x=2cosx\u7684\u5e73\u65b9-1=cosx\u7684\u5e73\u65b9-sinx\u5e73\u65b9=1-2sinx\u7684\u5e73\u65b9
cos2x\u7684\u51fd\u6570\u56fe\u50cf:
\u6269\u5c55\u8d44\u6599\uff1a
\u5e38\u7528\u516c\u5f0f\uff1a
\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+\u03b1\uff09=sin\u03b1 \uff08k\u2208Z\uff09
cos\uff082k\u03c0+\u03b1\uff09=cos\u03b1 \uff08k\u2208Z\uff09
tan\uff082k\u03c0+\u03b1\uff09=tan\u03b1 \uff08k\u2208Z\uff09
cot\uff082k\u03c0+\u03b1\uff09=cot\u03b1\uff08k\u2208Z\uff09
\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+\u03b1\uff09= \uff0dsin\u03b1
cos\uff08\u03c0+\u03b1\uff09=\uff0dcos\u03b1
tan\uff08\u03c0+\u03b1\uff09= tan\u03b1
cot\uff08\u03c0+\u03b1\uff09=cot\u03b1
\u516c\u5f0f\u4e09\uff1a
\u4efb\u610f\u89d2\u03b1\u4e0e-\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e4b\u95f4\u7684\u5173\u7cfb\uff08\u5229\u7528 \u539f\u51fd\u6570 \u5947\u5076\u6027\uff09\uff1a
sin\uff08\uff0d\u03b1\uff09=\uff0dsin\u03b1
cos\uff08\uff0d\u03b1\uff09= cos\u03b1
tan\uff08\uff0d\u03b1\uff09=\uff0dtan\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= sin\u03b1
cos\uff08\u03c0\uff0d\u03b1\uff09=\uff0dcos\u03b1
tan\uff08\u03c0\uff0d\u03b1\uff09=\uff0dtan\u03b1
cot\uff08\u03c0\uff0d\u03b1\uff09=\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-\u03b1\uff09= \uff0dsin\u03b1
cos\uff082\u03c0-\u03b1\uff09= cos\u03b1
tan\uff082\u03c0-\u03b1\uff09=\uff0dtan\u03b1
cot\uff082\u03c0-\u03b1\uff09=\uff0dcot\u03b1
\u516c\u5f0f\u516d\uff1a
\u03c0/2\u00b1\u03b1\u4e0e\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a
sin\uff08\u03c0/2+\u03b1\uff09=cos\u03b1
sin\uff08\u03c0/2\uff0d\u03b1\uff09=cos\u03b1
cos\uff08\u03c0/2+\u03b1\uff09=\uff0dsin\u03b1
cos\uff08\u03c0/2\uff0d\u03b1\uff09=sin\u03b1
tan\uff08\u03c0/2+\u03b1\uff09=\uff0dcot\u03b1
tan\uff08\u03c0/2\uff0d\u03b1\uff09=cot\u03b1
cot\uff08\u03c0/2+\u03b1\uff09=\uff0dtan\u03b1
cot\uff08\u03c0/2\uff0d\u03b1\uff09=tan\u03b1
\u63a8\u7b97\u516c\u5f0f\uff1a
3\u03c0/2 \u00b1 \u03b1\u4e0e\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a
sin\uff083\u03c0/2+\u03b1\uff09=\uff0dcos\u03b1
sin\uff083\u03c0/2\uff0d\u03b1\uff09=\uff0dcos\u03b1
cos\uff083\u03c0/2+\u03b1\uff09=sin\u03b1
cos\uff083\u03c0/2\uff0d\u03b1\uff09=\uff0dsin\u03b1
tan\uff083\u03c0/2+\u03b1\uff09=\uff0dcot\u03b1
tan\uff083\u03c0/2\uff0d\u03b1\uff09=cot\u03b1
cot\uff083\u03c0/2+\u03b1\uff09=\uff0dtan\u03b1
cot\uff083\u03c0/2\uff0d\u03b1\uff09=tan\u03b1
\u53c2\u8003\u8d44\u6599\uff1a\u4e09\u89d2\u51fd\u6570\u8bf1\u5bfc\u516c\u5f0f\u767e\u5ea6\u767e\u79d1
（根号2）cos(2x+45度）
-sin(2x-45)
√2(cos2x×√2/2-sin2x×√2/2)=√2(cosx×cosπ/4-sinπ/4)=√2cos(2x+π/4)
根据公式sin（a+b）=sinacosb+sinbcosa，
所以根号2*sin(2x+π/4)=（sin2xcosπ/4+sinπ/4cos2x)*根号2
=sin2x+cos2x
然后反过来看 就是你要的答案
绛旓細cos2x+sin2x =鈭2(鈭2/2*cos2x+鈭2/2*sin2x)=鈭2cos(2x-蟺/4)cos2x-sin2x =鈭2(鈭2/2*cos2x-鈭2/2*sin2x)=鈭2cos(2x+蟺/4)
绛旓細鍘熷紡=鈭2锛坰in蟺/4cos2X-cos蟺/4sin2X)=鈭2sin(蟺/4-2X),鍥犱负sin(蟺/4-2X)鐨勬渶澶у间负1銆佹渶灏忓间负-1,鎵浠x=鈭2sin(蟺/4-2X),鐨勬渶澶у间负鈭2銆佹渶灏忓间负-鈭2锛屾渶灏忔鍛ㄦ湡涓篢=2蟺/W=2蟺/2=蟺
绛旓細cos2x绛変簬鍟ワ細cos2X=(cosX)^2-(sinX)^2 cos2x鏄笁瑙掑嚱鏁颁腑鐨勪綑寮﹀嚱鏁扮殑骞虫柟锛屽嵆(cosx)^2銆備笅闈㈡槸瀵筩os2x鐨勭畻娉曞拰瑙ｆ瀽鐨勮В閲婏細绠楁硶锛1銆佷娇鐢ㄤ笁瑙掑嚱鏁扮殑鍊嶈鍏紡锛cos2x=cos^2x-sin^2x銆2銆佸皢cos^2x鍜宻in^2x琛ㄧず涓1-sin^2x锛屽嵆cos2x=1-2sin^2x銆傝В鏋愶細1銆乧os2x鍙互閫氳繃灏唜鐨勮搴﹀姞鍊嶆潵...
绛旓細y =sin2x-cos2x =鈭2.sin(2x-蟺/4)
绛旓細sin^2x-cos^2x锛-cos2x銆傚嵆cos2x=cos^2x-sin^2x绛夊紡涓ょ鍚屾椂涔樹互锛1锛屽氨寰楀埌sin^2x-cos^2x锛濓紞cos2x鍥犳寰楄瘉缁撹鎴愮珛銆傚洜涓烘牴鎹笁瑙掑嚱鏁扮殑浣欏鸡鍑芥暟鐨勫拰瑙掑叕寮忕煡cos(x+y)=cosxcosy-sinxsiny鎵浠ュ綋x锛漼鏃讹紝涓婇潰鐨勪綑寮﹀嚱鏁板拰瑙掑叕寮忔紨鍙樹负cos(x+x)=cosxcosx-sinxsinx銆備笁瑙掑嚱鏁拌蹇嗗彛璇 涓夎鍑芥暟...
绛旓細"cos2x"鍜"sin2x"鏄笁瑙掑嚱鏁颁腑鐨勪綑寮﹀拰姝ｅ鸡鍑芥暟锛屽綋涓や釜瑙掑害涔嬮棿瀛樺湪涓瀹氬叧绯绘椂锛岃繖涓や釜鍑芥暟浼氭湁鐗瑰畾鐨勫叧绯汇傚叿浣撴潵璇达紝閫氳繃涓夎鎭掔瓑寮忓彲浠ュ緱鍑轰互涓嬪叧绯伙細 cos2x = 1 - sin^2(2x) sin2x = 2sin(2x)cos(2x)
绛旓細渚濇嵁鍏紡锛sin2x=2sinxcosx cos2x=cos²x-sin²x
绛旓細sin2x鈥cos2x =鈭2[sin2xcos(蟺/4)鈥cos2xsin(蟺/4)]=鈭2sin(2x-蟺/4)
绛旓細鐢卞嶈鍏紡锛cos2x=cos²x-sin²x 寰楋細y=cos²2x-sin²2x=cos4x 绁濅綘寮蹇冿紒甯屾湜鑳藉府鍒颁綘锛屽鏋滀笉鎳傦紝璇疯拷闂紝绁濆涔犺繘姝ワ紒O(鈭鈭)O
绛旓細sinx^2*cos2x =(sin²x)'cos2x+sin²x(cos2x)'=2sinxcosxcos2x+sin²x(-2sin2x)=sin2xcos2x-2sin²xsin2x =sin2x(cos2x-2sin²x)=sin2x(1-4sin²x)
