Question : If $\tan \theta=\frac{8}{15}$, then the value of $\sqrt{\frac{1-\sin \theta}{1+\sin \theta}}$ is:
Option 1: $\frac{1}{5}$
Option 2: $\frac{3}{5}$
Option 3: $\frac{2}{5}$
Option 4: $\frac{4}{5}$
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Correct Answer: $\frac{3}{5}$
Solution :
$\tan \theta=\frac{8}{15}=\frac{\text{Perpendicular}}{\text{Base}}$
$\therefore$ Hypotenuse = $\sqrt{8^2+15^2}=\sqrt{289}= 17$
So, $\sin \theta=\frac{8}{17}$
$\sqrt{\frac{1-\sin \theta}{1+\sin \theta}}=\sqrt{\frac{1-\frac{8}{17}}{1+\frac{8}{17}}}=\sqrt{\frac{\frac{9}{17}}{\frac{25}{17}}}=\sqrt{\frac{9}{25}}=\frac{3}{5}$
Hence, the correct answer is $\frac{3}{5}$.
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