Question

$\sqrt{\frac{1+\sin \theta }{1-\sin \theta }}=$

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

Answer 1

Answer: (A)

$\sqrt{\frac{1+\sin \theta }{1-\sin \theta }}=\sqrt{\frac{(1+\sin \theta )(1+\sin \theta )}{(1-\sin \theta )(1+\sin \theta )}}$
$=\sqrt{\frac{(1+\sin \theta {)}^2}{1-{\sin }^2\theta }}$
$=\frac{1+\sin \theta }{\cos \theta }=\sec \theta +\tan \theta$