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{(1)/(3)} =(1)/(√(3)) \\ x=\tan^(-1)(1)/(√(3))= (\pi)/(6) \\ =n \pi-(5\pi)/(6),\ \ n\pi-(\pi)/(6)`