ctgx-sinx=2sin^2(x/2)

Так как 2sin^2(x/2)=1-cos x, ctg x=cos x/sin x, то

cos x-sin^2 x+sin x*cos x-sin x = 0.

(cos x-sin x) - sin x *(cos x-sin x)=0,

(cos x - sin x)*(1 - sin x) = 0.

1) sin x=1, x=PI/2+2n*PI,
2) cos x=sin x, tg x=1, x=PI/4+n*PI.