Question

Solution of $3({\sec }^2\theta +{\tan }^2\theta )=5$ is $\theta =n\pi \pm \frac{\pi }{m}$. Find $m$.

Answer 1

$3({\sec }^2\theta +{\tan }^2\theta )=5$
$\Rightarrow {\sec }^2\theta +{\tan }^2\theta =\frac{5}{3}$
$\Rightarrow {\tan }^2\theta =\frac{1}{3}={\left(\frac{1}{\sqrt{3}}\right)}^2$
$\Rightarrow \theta =n\pi \pm \frac{\pi }{6}$