Question

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

• A. $n\pi +\frac{\pi }{6}$
• 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 A $n\pi +\frac{\pi }{6}$

Simplifying $3\left({\sec }^2\theta +{\tan }^2\theta \right)=5$.

$3\left(\left(1+{\tan }^2\theta \right)+{\tan }^2\theta \right)=5$

$1+2{\tan }^2\theta =\frac{5}{3}$

$2{\tan }^2\theta =\frac{5}{3}-1$

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

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

$\tan \theta =\frac{1}{\sqrt{3}}$

$\tan \theta =\tan \frac{\pi }{6}$

$\theta =n\pi +\frac{\pi }{6}$