cos3x (sinx+1) = 0 (tg2x+1) (sin3x - √3:2) = 0

1. cos 3x * (sin x + 1) = 0

cos 3x = 0 или sin x + 1 = 0

cos 3x = 0

3x = π/2 + πK, K ϵ Z

x = π/6 + π/3K, K ϵ Z

sin x + 1 = 0

sin x = - 1

x = - π/2 + 2πK, K ϵ Z

Ответ: корни уравнения x = π/6 + π/3K, K ϵ Z или x = - π/2 + 2πK, K ϵ Z.

2. (tg 2x + 1) * (sin 3x - √3/2) = 0

tg 2x + 1 = 0 или sin 3x - √3/2 = 0

tg 2x = - 1

2x = arctg (-1) + πK, K ϵ Z

2x = - arctg 1 + πK, K ϵ Z

2x = - π/4 + πK, K ϵ Z

x = - π/8 + π/2K, K ϵ Z

sin 3x - √3/2 = 0

sin 3x = √3/2

3x = (-1) n * π/3 + πn, n ϵ Z

x = ((-1) n * π/3) / 3 + π/3n, n ϵ Z

Ответ: корни уравнения x = - π/8 + π/2K, K ϵ Z или x = ((-1) n * π/3) / 3 + π/3n, n ϵ Z.