Question

6tan^2x- 4sin^2x=1

Answer 1

6 sin^2 x / cos^2 x - 4 sin^2 x = 1
6 sin^2 x - 4 sin^2 x cos^2 x = cos^2 x
6 sin^2 x - 4 sin^2 x (1 - sin^2 x) = 1 - sin^2 x
let y = sin^2 x
6 y - 4 y ( 1 - y) = 1 - y
6y - 4 y + 4 y^2 = 1 - y
4 y^2 + 3 y - 1 = 0
(4 y - 1)( y +1) = 0
y = sin^2 x = 1/4
sin x = 1/2 or -1/2 so x = 30 or -30 degrees
or sin^2 x = -1 (how can square of any real number = -1 ? :)