Question

If $3\tan \theta =4$ then $\sqrt{\frac{1-\sin \theta }{1+\sin \theta }}$ is equal to

• A. $\frac{1}{2}$
• B. $\frac{2}{3}$
• C. $\frac{1}{3}$
• D. $Noneofthese$

Answer 1

The correct option is C $\frac{1}{3}$

$3\tan \theta =4$

$\tan \theta =\frac{4}{3}$

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

$\sin \theta =\frac{4}{5}=\sqrt{\frac{1-\frac{4}{5}}{1+\frac{4}{5}}}=\sqrt{\frac{1}{9}}$

$=\frac{1}{3}$