Solve 2sec^2(x) = 3 + tan(x) for 0 < x <pi/2

Make use of identity sech^2(x) = tan^2(x) + 1

=> 2{tan^2(x) + 1} = 3 + tan(x)

Multiply out brackets and rearrange

=> 2tan^2(x) - tan(x) - 1 = 0

Use quadratic formula with a = 2, b = -1, c = -1

=> tan(x) = (1 ± 3) / 4

But for the range of x given, tan(x) must be positive

=> x = arctan(1) = pi/4