Question

If $5\sin \theta =3$, then $\frac{\sec \theta +\tan \theta }{\sec \theta -\tan \theta }$ is equal to

• A. $\frac{1}{4}$
• B. $4$
• C. $2$
• D. $\frac{1}{2}$

Answer 1

The correct option is B $4$

sin $\theta =\frac{3}{5}$

$\frac{sec\theta +tan\theta }{sec\theta -tan\theta }$

Multiplying numerator and denominator by cos $\theta$

$\frac{sec\theta +tan\theta }{sec\theta -tan\theta }$ = $\frac{1+sin\theta }{1-sin\theta }$

$=$ $\frac{1+\frac{3}{5}}{1-\frac{3}{5}}$

Multiplying numerator and denominator by 5,

$=$ $\frac{5+3}{5-3}$

$=4$