sin3x - sin7x = 0

Перепишем sin7x в виде sin(3x + 4x):

sin3x - sin(3x + 4x) = 0

sin3x - (sin3xcos4x + cos3xsin4x) = 0

sin3x - sin3xcos4x - cos3xsin4x = 0

sin3x(1 - cos4x) - cos3x*sin4x = 0

sin3x(cos4x - 1) - cos3x*sin4x = 0

sin3x(-2sin(2x)^2 - 1) - 2cos(2x)sin3x = 0

sin3x(-2sin(2x)^2 - 1) + 2sin(2x)sin3x = 0

sin3x(-2sin(2x)^2 - 1 + 2sin(2x)) = 0

sin3x(-2sin(2x)^2 + 2sin(2x) - 1) = 0

sin3x(2sin(2x) - 1)^2 = 0

sin3x = 0 или 2sin(2x) - 1 = 0

sin3x = 0
3x = arcsin(0) + 2πk
3x = 0 + 2πk или 3x = π + 2πk
x = 0 + 2πk/3 или x = π/3 + 2πk/3

2sin(2x) - 1 = 0
sin(2x) = 1/2
2x = π/6 + 2πk или 2x = 5π/6 + 2πk
x = π/12 + πk или x = 5π/12 + πk

Ответ: x = 0 + 2πk/3, x = π/3 + 2πk/3, x = π/12 + πk или x = 5π/12 + πk, где k - любое целое число.