4cos^2x-5sinxcosx-6=0

Question

find the x :( please

Answer 1

since cos2x = 2cos^2 x - 1, we have

2cos2x - 5/2 sin2x - 4 = 0
or
4cos2x - 5sin2x - 8 = 0

4cos2x = 5sin2x + 8
16cos^2 2x = 25sin^2 2x + 80sin2x + 64
16 - 16sin^2 2x = 25sin^2 2x + 80sin2x + 64
41sin^2 2x + 80sin2x + 48 = 0

now just solve for sin2x using the quadratic formula.