Question

If $\tan \theta =\frac{1}{\sqrt{2}}$, find the value of $\frac{{\text{cosec}}^2\theta -{\sec }^2\theta }{{\text{cosec}}^2\theta +{\cot }^2\theta }$.

• A. $\frac{1}{10}$
• B. $\frac{2}{10}$
• C. $\frac{3}{10}$
• D. $\frac{4}{10}$

Answer 1

The correct option is C $\frac{3}{10}$

Given,

$\tan \theta =\frac{1}{\sqrt{2}}$

$\Rightarrow \csc \theta =\sqrt{3}$

$\Rightarrow \sec \theta =\frac{\sqrt{3}}{\sqrt{2}}$

$\Rightarrow \cot \theta =\sqrt{2}$

Given,

$\frac{{\csc }^2\theta -{\sec }^2\theta }{{\csc }^2\theta +{\cot }^2\theta }$

$=\frac{3-\frac{3}{2}}{3+2}$

$=\frac{3}{10}$