Решите уравнение

cos x - sin x = 4cos x * sin^2 х

cosx-sinx=2sin2xsinx

cosx-sinx=2*1/2 (cosx-cos3x)

cosx-sinx-cosx+cos3x=0

cos3x-sinx=0

cos3x-cos (π/2-x) = 0

-2sin (2x-π/4) sin (x+π/4) = 0

sin (2x-π/4) = 0⇒2x-π/4=πn⇒2x=π/4+πn⇒x=π/8+πn/2

sin (x+π/4) = 0⇒x+π/4=πn⇒x=-π/4+πn

2) 1/2sin2x=√3⇒sin2x=2√3

[-1; 1]-нет решения