Question

What is $\sqrt{\frac{1+\sin \theta }{1-\sin \theta }}$ equal to?

• A. $\sec \theta -\tan \theta$
• B. $sec\theta +\tan \theta$
• C. $\text{cose}c\theta +\cot \theta$
• D. $\text{cosec}\theta -\cot \theta$

Answer 1

Answer: (B)

$sec\theta +\tan \theta$

The value of $\sqrt{\frac{1+\sin \theta }{1-\sin \theta }}$ is equal to
$=\sqrt{\frac{(1+\sin \theta )}{(1-\sin \theta )}\times \frac{(1+\sin \theta )}{(1+\sin \theta )}}$
$=\frac{\sqrt{(1+\sin \theta {)}^2}}{\sqrt{1-{\sin }^2\theta }}$
$=\frac{1+\sin \theta }{\sqrt{{\cos }^2\theta }}$
$=\frac{1+\sin \theta }{\cos \theta }$
$=\sec \theta +\tan \theta$