若(sinθ+cosθ)/(sinθ-cosθ)=2,那么sin(θ-5π)*sin(3π/2-θ)的值是
问题描述：
若(sinθ+cosθ)/(sinθ-cosθ)=2,那么sin(θ-5π)*sin(3π/2-θ)的值是
A.3/4 B.±3/10 C.3/10 D.-3/10
我算出来是9/10 和答案都不一样、请问应该选什么、为什么、
答
(sinθ+cosθ)/(sinθ-cosθ)=2
2sinθ-2cosθ=sinθ+cosθ
sinθ=3cosθ
sin²θ+cos²θ=1
9cos²θ+cos²θ=1
cos²θ=1/10
sin(θ-5π)*sin(3π/2-θ)
=sin(θ+6π-5π)*sin(3π/2-θ-2π)
=sin(θ+π)*sin(-θ-π/2)
=(-sinθ)*[-sin(θ+π/2)]
=sinθ*sin(θ+π/2)
=sinθ*cosθ
=3cos²θ
=3/10
应该选C