0.5*sin2x*ctgx-cosx=sin^2x

Ctgx=cosx/sinx

sin2x=2sinx*cosx

0.5*sin2x*ctgx - cosx = sin^2 x

0.5*2*sinx*cosx*cosx/sinx - cox = 1 - cos^2 x

cos^2 x - cosx - 1 + cos^2 x = 0

2cos^2 x - cosx - 1 = 0

cosx = t

2t^2 - t - 1 = 0

D=1-4*2 * (-1) = 9

t1=1

t2=-0.5

1. cosx=1

2. cosx=-0.5

отсюда находим х