Question

化简(1-sinθ+cosθ/1-sinθ-cosθ)+(1-sinθ-cosθ)/(1-sinθ+cosθ)

Answer 1

通分
分子=(1+sinθ-cosθ)²+(1+sinθ+cosθ)²
=2(1+sinθ)²+2cos²θ
=2+4sinθ+2sin²θ+2cos²θ
=2+4sinθ+2
=4+4sinθ
=4(1+sinθ)

分母=(1+sinθ-cosθ)+(1+sinθ+cosθ)
=(1+sinθ)²-cos²θ
=1+2sinθ+sin²θ-cos²θ
=1+2sinθ+sin²θ-(1-sin²θ)
=2sinθ+2sin²θ
=2sinθ(1+sinθ)

所以原式=2/sinθ=2cscθ

Answer 2

显然sinθ≠1
(1-(sinθ-cosθ))/(1-(sinθ+cosθ))+(1-(sinθ+cosθ))/(1-(sinθ-cosθ))
=((1-(sinθ-cosθ))^2+(1-(sinθ+cosθ))^2)/((1-(sinθ-cosθ))(1-(sinθ+cosθ)))
=(4-4sinθ)/(1-2sinθ+(sinθ)^2-(cosθ)^2)
=(4-4sinθ)/(2(sinθ)^2-2sinθ)
=-2/sinθ

Answer 3

- - 不给悬赏