Question

Помогите решить уравнения a)1+cos2x=sin2x; b)sin3xsinx+cos3xcosx=-1.

Answer 1

1) sin^2x+cos^2x+cos^2x-sin^2x = 2sinxcosx
cos^2x = sinxcosx
cosx(cosx-sinx) = 0
cosx = 0 => x = π/2 + πn
cosx = sinx => 1 = tgx => x = π/4+πn
2)sin3xsinx+cos3xcosx=1
cos(3x-x) = 1
cos2x = 1
2x = 2πn
x = πn