Question

If $\tan \theta =\frac{1}{\sqrt{7}}$ and $\theta$ is an acute angle, find $\frac{{\text{cosec}}^2\theta -{\sec }^2\theta }{{\text{cosec}}^2\theta +{\sec }^2\theta }$.

• A. $\frac{3}{4}$
• B. $\frac{1}{2}$
• C. $2$
• D. $\frac{5}{4}$

Answer 1

The correct option is A $\frac{3}{4}$

$tan\theta =\frac{1}{\sqrt{7}}$

=> $cosec\theta =\sqrt{8}$ and $sec\theta =\frac{\sqrt{8}}{\sqrt{7}}$

Putting these values in the given expression, we get the value as $\frac{3}{4}$