Решить уравнение: tgx-sinx=2sin^2 (x/2)

Sinx/cosx - sinx=2 * (1-cosx) / 2

(sinx-sinxcosx) / cosx=1-cosx

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

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

cosx≠0⇒ (1-cosx) (sinx-cosx) = 0

1-cosx=0⇒cosx=1⇒x=2πn

sinx-cosx=0/cosx≠0

tgx-1=0⇒tgx=1⇒x=π/4+πn