Question

If $\tan \theta =\frac{1}{\sqrt{7}}$, find the value of $\frac{cose{c}^2\theta -{\sec }^2\theta }{cose{c}^2\theta +{\sec }^2\theta }$.

Answer 1

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

$\frac{{\text{cosec}}^2\theta -{\sec }^2\theta }{{\text{cosec}}^2\theta +{\sec }^2\theta }$

$=\frac{1-{\tan }^2\theta }{1+{\tan }^2\theta }$

$=\frac{1-\frac{1}{7}}{1+\frac{1}{7}}$

$=\frac{6}{8}$

$=\frac{3}{4}$