Question

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

要过程喔~

Answer 1

(1+cosθ-sinθ)/(1-cosθ-sinθ)+(1-cosθ-sinθ)/(1+cosθ-sinθ)
=(1+2cos^2θ/2-1-2sinθ/2*cosθ/2)/(1-[1-2sin^2θ/2]-2sinθ/2*cosθ/2)+(1-[1-2sin^2θ/2]-2sinθ/2*cosθ/2)/(1+2cos^2θ/2-1-2sinθ/2*cosθ/2)
=2cosθ/2[cosθ/2-2sinθ/2]/2sinθ/2[sinθ/2-cosθ/2]+2sinθ/2[sinθ/2-cosθ/2]/2cosθ/2[cosθ/2-2sinθ/2]
=-cosθ/2/sinθ/2-sinθ/2/cosθ/2
=-(cos^2θ/2+sin^2θ/2)/sinθ/2*cosθ/2
=-2/sinθ

Answer 2

(1+cosθ-sinθ)/(1-cosθ-sinθ)+(1-cosθ-sinθ)/(1+cosθ-sinθ)
=(2cos^2 θ/2-2sinθ/2cosθ/2)/(2sin^2 θ/2-2sinθ/2cosθ/2)+(2sin^2 θ/2-2sinθ/2cosθ/2)/(2cos^2 θ/2-2sinθ/2cosθ/2)
=2cosθ/2(cosθ/2-sinθ/2) / 2sinθ/2(sinθ/2-cosθ/2)+2sinθ/2(sinθ/2-cosθ/2) / 2cosθ/2(cosθ/2-sinθ/2)
=-cosθ/2 / sinθ/2-sinθ/2 / cosθ/2
=-（cos^2 θ/2+sin^2 θ/2) / sinθ/2cosθ/2
=-2/sinθ