Question

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

• A. $\frac{1}{5}$
• B. $\frac{2}{5}$
• C. $\frac{3}{5}$
• D. None

Answer 1

The correct option is C $\frac{3}{5}$

$\cot \theta =\frac{1}{\sqrt{3}}$
$\cot \theta =\cot {60}^{\circ }$
$\theta ={60}^{\circ }$
Now, $\frac{1-{\cos }^2\theta }{2-{\sin }^2\theta }$
= $\frac{1-{\cos }^{2}60}{2-{\sin }^{2}60}$
= $\frac{1-(\frac{1}{2}{)}^2}{2-(\frac{\sqrt{3}}{2}{)}^2}$
= $\frac{4-1}{8-3}$
= $\frac{3}{5}$