Question

ПОМОГИТЕ,ПОЖАЛУЙСТА!!!

Решите уравнение.

1)3sin2x + sin x=0

2)cos3x+cos x=0

Answer 1

1) 3*2sinx*cosx + sinx = 0
sinx*(6cosx + 1) = 0
sinx = 0, x = πk
cosx = -1/6, x = +-arccos(-1/6) + 2πk
2) cos(3x) = cos(x + 2x) = cos(2x)*cosx - sin(2x)*sinx = (2cos^2 x - 1)*cosx - 2cosx*(1 - cos^2(x)) = 2cos^3(x) - cosx - 2cosx + 2cos^3(x) = 4cos^3(x) - 3cosx
4cos^3(x) - 3cosx + cosx = 0
cosx*(4cos^2(x) - 2) = 0
cosx = 0, x = π/2 + πk
cos^2(x) = 1/2, cosx = √2/2, x = +-π/4 + 2πk; cosx = -√2/2, x = +-3π/4 + 2πk