Решить пример: sin3x+sin7x-sin5x-sinx=0

sin3x+sin7x-sin5x-sinx=0
2cos2xsinx+2cos6xsinx=0
sinx(cos2x+cos6x)=0

sinx=0
x=πk

cos2x+cos6x=0
cos4xcos2x=0

cos4x=0
4x=π/2+πk
x=π/8+πk/4

cos2x=0
2x=π/2+πk
x=π/4+πk/2

ответ: x=π/4+πk/2, x=π/8+πk/4, x=πk; k∈Z