(1+sinθ)/cosθ=-1/2 求cosθ/(sinθ-1)的值

解;
(1+sinb)/cosb=-cosb/(sinb-1)
可以证明的;
因为;
(sinb+1)(sinb-1)
=sinb^2-1=-cosb^2
所以上式是成立的:

所以:
cosb/(sinb-1)
=-(1+sinb)/cosb
=1/2

(1+sinθ)/cosθ=-1/2
分子分母都乘以sinθ-1
[(1+sinθ)(sinθ-1)]/[cosθ(sinθ-1)]=-1/2
(sin²θ-1)/[cosθ(sinθ-1)]=-1/2
-cos²θ/[cosθ(sinθ-1)]=-1/2
-cosθ/(sinθ-1)=-1/2
cosθ/(sinθ-1)=1/2

(1+sinθ)/cosθ=-1/2
(1+cos(90-θ))/sin(90-θ)=-1/2

sin(90-θ)/(1+cos(90-θ))=tan((90-θ)/2)=-2

cosθ/(sinθ-1)
=sin(90-θ)/(cos(90-θ)-1)
=-1/tan((90-θ)/2)
=1/2

(1+sinθ)/cosθ=cosθ/(1-sinθ)=-1/2,则cosθ/(sinθ-1)=1/2

上下同乘1-sinθ，得cosθ/(sinθ-1)=1/2

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