(1-sinx)/cosx 化简成tanx/2的式子

\u5316\u7b80\uff1bSINx/\uff081-COSx\uff09*\u6839\u53f7\uff08TANx-SINx/TANx+SINx\uff09

\u5982\u679c\u8981\u5316\u7b80\u7684\u5f0f\u5b50\u4e3a
SINx/\uff081-COSx\uff09*\u6839\u53f7[(TANx-SINx)/(TANx+SINx)]
\u5316\u7b80\u5982\u56fe

\u89e3\uff1a\u7b54\u6848\u4e3a 1 \u56e0\u4e3a(sinx)^2 +(cosx)^2 =1
sinx-1/sinx=[(sinx)^2-1]/sinx=[-(cosx)^2]/sinx
cox-1/cosx=[-(sinx)^2]/cosx
\u9898\u76ee\u4e2d\u524d\u4e24\u4e2a\u5c0f\u62ec\u53f7\u76f8\u4e58\u7b49\u4e8e
sinxcosx \u6b64\u5f0f\u5b50\u5206\u6bcd\u770b\u4f5c1\uff0c
\u5373\u662f\uff0c\uff08sinxcosx)/[(sinx)^2+(cosx)^2]
\u5316\u7b80\u5373\u662f \u9898\u76ee\u4e2d\u7b2c\u4e09\u4e2a\u5c0f\u62ec\u53f7\u4e2d\u7684\u9879\u7684\u5012\u6570
\u56e0\u6b64\u76f8\u4e58\u5f97 1

解答:
(1-sinx)/cosx
=[sin²(x/2)+cos²(x/2)-2sin(x/2)cos(x/2)]/[cos²(x/2)-sin²(x/2)]
=[cos(x/2)-sin(x/2)]²/{[cos(x/2)+sin(x/2)]*[cos(x/2)-sin(x/2)]}
=[cos(x/2)-sin(x/2)]/[cos(x/2)+sin(x/2)]
分子分母同时除以cos(x/2)
=[1-tan(x/2)]/[1+tan(x/2)]

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