已知cos（π/4+x)=-3/5,3/4π＜x＜5π/4,求(sin2x+2sin²x)/(1-tanx)的值.
网友回答
cos(π/4+x)
=cosπ/4cosx-sinπ/4sinx
=(√2/2)(cosx-sinx)
=-3/5cosx-sinx=-3√2/5
(cosx-sinx)²=18/25
1-2sinxcosx=18/25
2sinxcosx=7/25
(sinx+cosx)²=1+2sinxcosx=1+7/25=32/25
又∵3/4π＜x＜5π/4
∴sinx+cosx