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
RM
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