已知cos（π/4+x)=3/5,5/4π＜x＜7π/4,求(sin2x+2sin²x)/(1-tanx)

cos（π/4+x)=3/5,3/2π＜π/4+x＜2π,所以sin（π/4+x)=-4/5,Sin2x=-cos(π/2+2x)=-cos[2(π/4+x)]=-[1-2sin²(π/4+x)]=7/25。sinx+cosx=√2* sin（π/4+x)=-4√2/5,cosx –sinx=√2* cos（π/4+x)=3√2/5,(sin2x+2(sinx)^2)/(1-tanx)=[2sinx(sinx+cosx)]/(1-sinx/cosx)……分子分母同乘以cosx可得下式=[2sinx cosx (sinx+cosx)]/( cosx -sinx)=[sin2x (sinx+cosx)]/( cosx -sinx)=[7/25*(-4√2/5)]/(3√2/5)=-28/75。