1 - cosX = tgX - sinX

1-cosx=tgx-sinx

1-cosx = (sinx/cosx) - sinx ОДЗ: сosx≠0 x≠π/2+πn.

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

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

(1-cosx) * (tgx-1) = 0

1-cosx=0

cosx=1

x₁=2πn

tgx-1=0

tgx=1

x₂=π/4+πn.

Ответ: x₁=2πn x₂=π/4+πn.

[-2π; 3π] x=-2π; 0; 2π; - 7π/4; - 3π/4; π/4; 5π/4; 9π/4; 13π/4.