Question

已知sinθ+cosθ/sinθ-cosθ=2 求sin(θ-5π)sin(3π/2-θ) 答案是多少

Answer 1

sinθ+cosθ/sinθ-cosθ=2
分子分母同除以cosθ，得
（tanθ+1）/(tanθ-1)=2
（tanθ+1）=2(tanθ-1)
即tanθ=3

所以
sin(θ-5π)sin(3π/2-θ)
=-sinθ(-cosθ)
=sinθcosθ
=1/2sin2θ
=tanθ/(1+tan²θ)
=3/(1+3²)
=3/10

Answer 2

转：

(sinθ+cosθ)/(sinθ-cosθ)=2
sinθ+cosθ=2(sinθ-cosθ)
3cosθ=sinθ
tanθ=3

sin(θ-5π)cos(3π/2-θ)
=(-sinθ)*(-sinθ)
=sin²θ
=(1-cos2θ)/2
=1/2-1/2*cos2θ
=1/2-1/2*(1+tan²θ)/(1-tan²θ)
=1/2-1/2*(1+3²)/(1-3²)
=9/8

Answer 3

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