1+tanx为什么等于sinx+cosx？ 1加tanx等于什么？
1+tanx\u5982\u4f55\u5316\u7b80\u6210cosx+sinx\u65e0\u6cd5\u5316\u7b80\u3002
1+tanx
=1+sinx/cosx
=cosx/cos+sinx/cosx
=(cosx+sinx)/cosx
\u2260cosx+sinx
\u5982\u679c1+tanx=cosx+sinx\u5219
(cosx+sinx)/cosx=cosx+sinx
(cosx+sinx)/cosx-(cosx+sinx)=0
(cosx+sinx)(1/cosx-1)=0
(1) cosx+sinx=0
(\u221a2/2)cosx+(\u221a2/2)sinx=0
sin(\u03c0/4)cosx+cos(\u03c0/4)sinx=0
sin(\u03c0/4+x)=0
\u03c0/4+x=0
x=k\u03c0-\u03c0/4
(2) 1/cosx-1=0
1/cosx=1
cosx=1
x=(2k+1)\u03c0
\u222btanxdx\uff1d\u222b\uff08sinx/cosx\uff09dx\uff1d\uff0d\u222b\uff081/cosx\uff09d\uff08cosx\uff09\uff1d\uff0dln\uff5ccosx\uff5c\uff0bC\u3002
\u5728Rt\u25b3ABC\uff08\u76f4\u89d2\u4e09\u89d2\u5f62\uff09\u4e2d\uff0c\u2220C=90\u00b0\uff0cAB\u662f\u2220C\u7684\u5bf9\u8fb9c\uff0cBC\u662f\u2220A\u7684\u5bf9\u8fb9a\uff0cAC\u662f\u2220B\u7684\u5bf9\u8fb9b\uff0c\u6b63\u5207\u51fd\u6570\u5c31\u662ftanB=b/a\uff0c\u5373tanB=AC/BC\u3002
\u7531\u4e8e\u4e09\u89d2\u51fd\u6570\u7684\u5468\u671f\u6027\uff0c\u5b83\u5e76\u4e0d\u5177\u6709\u5355\u503c\u51fd\u6570\u610f\u4e49\u4e0a\u7684\u53cd\u51fd\u6570\u3002\u4e09\u89d2\u51fd\u6570\u5728\u590d\u6570\u4e2d\u6709\u8f83\u4e3a\u91cd\u8981\u7684\u5e94\u7528\u3002\u5728\u7269\u7406\u5b66\u4e2d\uff0c\u4e09\u89d2\u51fd\u6570\u4e5f\u662f\u5e38\u7528\u7684\u5de5\u5177\u3002
\u5728Rt\u25b3ABC\u4e2d\uff0c\u5982\u679c\u9510\u89d2A\u786e\u5b9a\uff0c\u90a3\u4e48\u89d2A\u7684\u5bf9\u8fb9\u4e0e\u90bb\u8fb9\u7684\u6bd4\u503c\u968f\u4e4b\u786e\u5b9a\uff0c\u8fd9\u4e2a\u6bd4\u53eb\u505a\u89d2A\u7684\u6b63\u5207\uff0c\u8bb0\u4f5ctanA\u3002
\u5373\uff1atanA=\u2220A\u7684\u5bf9\u8fb9/\u2220A\u7684\u90bb\u8fb9\u3002
\u540c\u89d2\u4e09\u89d2\u51fd\u6570\uff1a
\uff081\uff09\u5e73\u65b9\u5173\u7cfb\uff1a
sin^2(\u03b1)+cos^2(\u03b1)=1\u3002
tan^2(\u03b1)+1=sec^2(\u03b1)\u3002
cot^2(\u03b1)+1=csc^2(\u03b1)\u3002
\uff082\uff09\u79ef\u7684\u5173\u7cfb\uff1a
sin\u03b1=tan\u03b1*cos\u03b1 cos\u03b1=cot\u03b1*sin\u03b1\u3002
tan\u03b1=sin\u03b1*sec\u03b1 cot\u03b1=cos\u03b1*csc\u03b1\u3002
sec\u03b1=tan\u03b1*csc\u03b1 csc\u03b1=sec\u03b1*cot\u03b1\u3002
\uff083\uff09\u5012\u6570\u5173\u7cfb\uff1a
tan\u03b1\u00b7cot\u03b1=1\u3002
sin\u03b1\u00b7csc\u03b1=1\u3002
cos\u03b1\u00b7sec\u03b1=1\u3002
= 1 + sinx/cosx
= sinx/cosx + 1
= (sinx + cosx)/cosx
上面这个公式才是正确的。
sin：a/c，∠A的对边比斜边
cos：b/c，∠A的邻边比斜边
tan：a/b，······
1+a/b=括号a+b/b
a/c+b/c=括号a+b/c
相等吗？
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