Question

Solve the equations
$3({\sec }^2\theta +{\tan }^2\theta )=5$.

Answer 1

Consider the given equation.

$3({\sec }^2\theta +{\tan }^2\theta )=5$

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

We know that

${\sec }^2\theta =1+{\tan }^2\theta$

Therefore,

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

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

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

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

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

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

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

Hence, this is the answer.