Question

sin 3 x + sin x / cos x = 0

Answer 1

Решение
(sin3x + six) / cosx = 0
(3sinx - 4sin^3x + sinx) / cosx = 0
sinx(3 - 4sin^2x + 1 ) / cosx = 0
4*tgx * (1 - sin^2x) = 0
1)  tgx = 0
x1 = πn, n∈Z
2)  1 - sin^2x = 0
sin^2x = 1
sinx = -1
x2 = - π/2 + 2πm, m∈Z
sinx = 1
x3 = π/2 + 2πk, k∈Z
Ответ: x1 = πn, n∈Z;  x2 = - π/2 + 2πm, m∈Z;  x3 = π/2 + 2πk, k∈Z.