Question

1 - cosX = tgX - sinX

Answer 1

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.