Question

If ${\tan }^2\theta =\frac{1}{3},$ then find the value of $\cos \theta$

Answer 1

${\tan }^2\theta =\frac{1}{3}$

$\Rightarrow 1+{\tan }^2\theta =1+\frac{1}{3}$

$\Rightarrow {\sec }^2\theta =\frac{3+1}{3}$

$\Rightarrow {\sec }^2\theta =\frac{4}{3}$

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

$\Rightarrow \frac{1}{\cos \theta }=\pm \frac{2}{\sqrt{3}}$

$\therefore \cos \theta =\pm \frac{\sqrt{3}}{2}$