Prove.1+ A 1- A =c o A+1 c o A-1 - Vidyadip

Question

Prove.$\frac{1+\sin A}{1-\sin A}=\frac{c o \sec A+1}{c o \sin A-1}$

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Answer

$\begin{aligned} & \text { R.H.S }=\frac{\frac{1}{\sin A}+1}{\frac{1}{\sin A}-1} \\ & =\frac{\frac{1+\sin A}{\sin A}}{\frac{1-\sin A}{\sin A}} \\ & =\frac{(1+\sin A)}{\sin A} \times \frac{\sin A}{(1-\sin A)} \\ & =\frac{1+\sin A}{1-\sin A} \\ & \therefore \text { R.H.S = L.H.S }\end{aligned}$

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