Пожалуйста помогите ) sin 10x = sin 2x

Question

Пожалуйста помогите )

sin 10x = sin 2x

Answer 1

Sin(x) + sin(2x) + sin(3x) = cos(x) + cos(2x) + cos(3x) 
sin(2x) + sin(2x – x) + sin(2x + x) = cos(2x) + cos(2x – x) + cos(2x + x) 
sin(2x) + sin(2x)·cos(x) – cos(2x)·sin(x) + sin(2x)·cos(x) + cos(2x)·sin(x) = 
= cos(2x) + cos(2x)·cos(x) + sin(2x)·sin(x) + cos(2x)·cos(x) – sin(2x)·sin(x) 
sin(2x) + 2·sin(2x)·cos(x) = cos(2x) + 2·cos(2x)·cos(x) 
sin(2x)·[1 + 2·cos(x)] = cos(2x)·[1 + 2·cos(x)] 
[sin(2x) – cos(2x)]·[1 + 2·cos(x)] = 0 

Comments

1) sin(2x) – cos(2x) = 0
sin(2x) = cos(2x)
tg(2x) = 1
2x = π/4 + π·n = π(4n + 1)/4
x = π(4n + 1)/8

2) 1 + 2·cos(x) = 0
cos(x) = –½
x = ±2π/3 + 2·π·n = 2π(3n ± 1)/3

Ответ:
{x = π(4n + 1)/8
{x = 2π(3n ± 1)/3
n — целое.