sin^2(θ)+4cosθ/sin(90-θ) -1/tan(90-θ)

问题描述:

sin^2(θ)+4cosθ/sin(90-θ) -1/tan(90-θ)

sin^2(θ)+4cosθ/sin(90-θ) -1/tan(90-θ)
=sin^2θ+4cosθ/cosθ-1/cotθ
=sin^2θ+4-tanθ

[sin^2(θ)+4cosθ]/sin(90-θ)-1/tan(90-θ)
=[sin^2(θ)+4cosθ]/cos(θ)-1/cotθ
=[sin^2(θ)+4cosθ]/cos(θ)-sin(θ)/cosθ
=[sin^2(θ)-sinθ+4cosθ]/cosθ
={sin(θ)[sin(θ)-1]+4cosθ]/cosθ
=tanθ(sinθ-1)+4