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