sin 5x sin x =sin 7x sin 3x

Question

sin 5x sin x =sin 7x sin 3x

Answer 1

1/2 (cos(4 x)-cos(6 x)) = 1/2 (cos(4 x)-cos(10 x))

 sin^2(x) (2 cos(2 x)+2 cos(4 x)+1) = sin^2(x) (2 cos(2 x)+1) (2 cos(2 x)+2 cos(4 x)+2 cos(6 x)+1)

 

 x = 0       x = pi n, n element Z

 x = -pi      x = pi n-pi/2, n element Z