Question

If $x$ is acute, then $\sqrt{\frac{1+\sin x}{1-\sin x}}$ is

• A. $\sec x+\tan x$
• B. $co\sec x+\cot x$
• C. $\sec x+co\sec x$
• D. $\tan x+\cot x$

Answer 1

The correct option is A $\sec x+\tan x$

Given expression
$=\frac{\sqrt{1+\sin x}\times \sqrt{1+\sin x}}{\sqrt{1-\sin x}\times \sqrt{1+\sin x}}$
$=\frac{1+\sin x}{\sqrt{1-{\sin }^{2}x}}=\frac{1+\sin x}{\cos x}$
$=\sec x+\tan x$