Cos2x=sinx-cosx тригонометрическое уравнение

Cos²x-sin²x - (sinx-cosx) = 0

(cosx-sinx) (cosx+sinx) + (cosx-sinx) = 0

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

cosx-sinx=0/cosx

1-tgx=0

tgx=1

x=π/4+πn, n∈z

cosx+sinx+1=0

2cos² (x/2) + 2sin (x/2) cos (x/2) = 0

2cos (x/2) * (cos (x/2) + sin (x/2) = 0

cos (x/2) = 0

x/2=π/2+πk

x=π+2πk, k∈z

cos (x/2) + sin (x/2) = 0/cos (x/2)

1+tg (x/2) = 0

tg (x/2) = - 1

x/2=-π/4+πm

x=-π/2+2πm, m∈z