Question

If $\cot \theta =\frac{1}{\sqrt{3}}$. find the value of $\frac{1-{\cos }^2\theta }{2-{\sin }^2\theta }$

Answer 1

Given : $\cot \theta =\frac{1}{\sqrt{3}}\Rightarrow \theta =\frac{\pi }{3}$

$\therefore \sin \frac{\pi }{3}=\frac{\sqrt{3}}{2}$ and $cos\frac{\pi }{3}=\frac{1}{2}$

$\to \frac{1-{\cos }^2\theta }{2-{\sin }^2\theta }=\frac{1-\frac{1}{4}}{2-\frac{3}{4}}=\frac{3}{5}$