Question

If $3({\sec }^2\theta +{\tan }^2\theta )=5$, then the general value of $\theta$ is -

• A. $2n\pi +\frac{\pi }{6}$
• B. $2n\pi \pm \frac{\pi }{6}$
• C. $n\pi \pm \frac{\pi }{6}$
• D. $n\pi \pm \frac{\pi }{3}$

Answer 1

The correct option is C $n\pi \pm \frac{\pi }{6}$

$3({\tan }^2\theta +{\text{sec}}^2\theta )=5⟹3(1+2{\tan }^2\theta )=5⟹{\tan }^2\theta =\frac{1}{3}$

$⟹\theta =n\pi \pm \frac{\pi }{6}$