cos^2x-sinxcosx-1/2=o

Answer 1

dropping the x's for brevity,

2cos^2 - 1 = 2sin cos
4cos^4 - 4cos^2 + 1 = 4sin^2 cos^2
4cos^4 - 4cos^2 + 1 = 4(1-cos^2) cos^2
4cos^4 - 4cos^2 + 1 = 4cos^2 - 4cos^4
8cos^4 - 8cos^2 + 1 = 0
cos^2 = 1/4 (2 ± √2)
x = kπ/2 ± π/8 for integer k