Question

Prove that $\sqrt{\frac{1+\sin x}{1-\sin x}}=\sec x+\tan x$

Answer 1

$\sqrt{\frac{1+\sin x}{1-\sin x}}$

$=\frac{\sqrt{1+\sin x}}{\sqrt{1-\sin x}}\times \frac{\sqrt{1+\sin x}}{\sqrt{1+\sin x}}$

$=\frac{1+\sin x}{\sqrt{1-{\sin }^{2}x}}$

$=\frac{1+\sin x}{\cos x}$

$=\frac{1}{\cos x}+\frac{\sin x}{\cos x}$

$=\sec x+\tan x$