# (1-sinA+cosA)/(sinA+cosA-1)=(1+cosA)/sinA

Trigonometry equalities, inequalities and expressions - sin, cos, tan, cot

### (1-sinA+cosA)/(sinA+cosA-1)=(1+cosA)/sinA

Solve the trigonometric equation:
$$\frac{1-\sin A+\cos A}{\sin A+\cos A-1}= \frac{1+\cos A}{\sin A}$$
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### Re: (1-sinA+cosA)/(sinA+cosA-1)=(1+cosA)/sinA

To save typing let $$s=\sin A$$ and $$c=\cos A$$
$$(1-s+c)s = s-s^2+sc+(-1+s^2+c^2)+(c-c) = s+c-1+sc+c^2-c +(s^2-s^2) = (s+c-1)(1+c)$$
Since
$$(1-s+c)s = (s+c-1)(1+c)$$
we know that
$$\frac{1-s+c}{s+c-1} = \frac{1+c}{s}$$
provided that $$s\ne 0$$, and $$s+c-1\ne 0$$ (which occur when $$A=\pi n$$ or $$\pi/2+2\pi n$$ for some integer $$n$$).

Hope this helped,

R. Baber.
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### Re: (1-sinA+cosA)/(sinA+cosA-1)=(1+cosA)/sinA

Thank you very much.
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