化简(1/sinx+1/tanx)(1-cosx)=? 请给出详细的化简过程，谢谢！ 1+tanx如何化简成cosx+sinx
\u5316\u7b80\uff0c(1/sinx+1/tanx)*(1-cosx)= \u6c42\u89e3\u9898\u5168\u8fc7\u7a0b\u6211\u7684\u8fc7\u7a0b\u5982\u56fe
\u65e0\u56fe\u8bf7\u8ffd\u95ee
\u5982\u679c\u4f60\u8ba4\u53ef\u6211\u7684\u56de\u7b54\uff0c\u8bf7\u70b9\u51fb\u201c\u91c7\u7eb3\u56de\u7b54\u201d\uff0c\u795d\u5b66\u4e60\u8fdb\u6b65\uff01
\u624b\u673a\u63d0\u95ee\u7684\u670b\u53cb\u5728\u5ba2\u6237\u7aef\u53f3\u4e0a\u89d2\u8bc4\u4ef7\u70b9\u3010\u8bc4\u4ef7\u3011\uff0c\u7136\u540e\u5c31\u53ef\u4ee5\u9009\u62e9\u3010\u6ee1\u610f\uff0c\u95ee\u9898\u5df2\u7ecf\u5b8c\u7f8e\u89e3\u51b3\u3011\u4e86
\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
=(1+cosx)(1-cosx)/sinx
=[1-(cosx)的平方]/sinx
=(sinx)的平方/sinx
=sinx
原式=[1/sinx+1/(sinx/cosx)(1-cosx)
=[1/sinx+cosx/sinx](1-cosx)
=[(1+cosx)/sinx](1-cosx)
=[(1+cosx)(1-cosx)]/sinx
=[1-cos²x]/sinx
=sin²x/sinx
=sinx。
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