Question

Solve 2 sec^2 x + tan^2 x - 3=0.

Answer 1

2 sec^2 x + tan^2 x - 3 = 0
2(1 + tan^2 x) + tan^2 x - 3 = 0              [sec^2 x = 1 + tan^2 x]
2 + 2tan^2 x + tan^2 x - 3 = 0
3tan^2 x = 1
tan^2 x = 1/3

$\tan x = \pm \sqrt{\frac{1}{3}} =\frac{1}{\sqrt{3}} \\ x=\tan^{-1}\frac{1}{\sqrt{3}}= \frac{\pi}{6} \\ =n \pi-\frac{5\pi}{6},\ \ n\pi-\frac{\pi}{6}$