Question

Решить уравнение:
$sinxsin3x+sin4xsin8x=0$

Answer 1

[Cos(x-3x) - Cos(x+3x)]/2  + [Cos(4x-8x) - Cos(4x+8x)]/2 = 0
Cos2x - Cos4x + Cos4x - Cos12x= 0
Cos2x - Cos12x = 0
- 2 Sin[(2x + 12x)/2]Sin[(2x - 12x)/2]= 0
Sin7xSin5x = 0
Sin7x = 0
7x = Пn, n э z
x = Пn/7, n э z
Sin5x = 0
5x = Пn, n э z
x = Пn/5, nэ z
Ответ: Пn/5, Пn/7, n э z