(sinθ+cosθ)/(sinθ-cosθ)=2,则sin(θ-5π)*sin(3π/2-θ)=

题目

(sinθ+cosθ)/(sinθ-cosθ)=2,则sin(θ-5π)*sin(3π/2-θ)=

答案

(sinθ+cosθ)/(sinθ-cosθ)=2sinθ+cosθ =2sinθ-2cosθ3cosθ =sinθsinθ与cosθ同号两边平方：9cos^2θ =sin^2θ9cos^2θ =1-cos^2θcos^2θ =1/10|cosθ|=1/根号10|sinθ|=3|cosθ|=3/根号10sin(θ-5π)*sin(...