2cos^2x-7cosx=2sin^2x

2cos^2 (x) - 7cos (x) = 2sin^2 (x)

2cos^2 (x) - 7cos (x) - 2 (1-cos^2 (x)) = 0

4cos^2 (x) - 7cos (x) - 2=0

cos (x) = t

4*t^2-7t-2=0

D=b^2-4ac=81

t1 = (7-9/8=-1/4

t2 = (7+9) / 8=2>1 - не подходит.

cos (x) = - 1/4

x=±arccos (-1/4) + 2*pi*n