Sin7x=sinx помогите !!!!!

Question

Sin7x=sinx помогите !!!!!

Answer 1

Sin7x - sinx = 0
2*[cos(7x+x)/2]*[sin(7x-x)] /2= 0
1)  cos(7x+x)/2 = 0
cos4x = 0
4x = π/2 + πn, n∈Z
x1 = π/8 + πn/4, n∈Z
 2)  sin(7x-x)/2 = 0
sin(3x) = 0
3x = π/2 + πk, k∈Z
x2 = π/6 + πk/3, k∈Z