Решите тригонометрическое уравнение sin3x+sin7x=-sin11x

Sin3x+Sin7x=-Sin11x

Sin3x+Sin7x + Sin11x = 0

(Sin3x + Sin11x) + Sin7x = 0

2Sin7xCos4x + Sin7x = 0

Sin7x (2Cos4x + 1) = 0

Sin7x = 0 или 2 Сos4x + 1 = 0

7x = πn, n ∈ Z Cos4x = - 1/2

x = πn/7, n ∈Z 4x = + - arcCos (-1/2) + 2πk, k ∈Z

4x = + - 2π/3 + 2πk, k ∈Z

x = + - π/6 + πk/2, k ∈ Z