cos^2x - 1/2sin2x + cosx = sinx

cos^2x - 1/2sin2x + cosx = sinx

sin2x = 2sinx*cosx

cos^2x - 1/2*2sinx*cosx+cosx = sinx

cos^2x - 1/2*2sinx*cosx+cosx - sinx = 0

cos^2x-sinx*cosx+cosx-sinx=0

cosx (cosx+1) - sinx (cosx+1) = 0

(cosx+1) * (cosx-sinx) = 0

cosx+1=0 - > cosx = - 1 - > x=pi+2pi*K

cosx-sinx=0 Делим уравнение на корень из 2

sin (pi/4-x) = 0

pi/4-x=pi*n

x=pi/4-pi*n