sin3x+sinx=0

Sure, let's solve the equation step by step.

1. Rewrite the equation: sin3x + sinx = 0

2. Use the identity for sin3x which is 3sinx - 4sin^3x. So the equation becomes: 3sinx - 4sin^3x + sinx = 0

3. Combine like terms: 4sinx - 4sin^3x = 0

4. Factor out 4sinx: 4sinx(1 - sin^2x) = 0

5. Set each factor equal to zero and solve for x:

   For 4sinx = 0, sinx = 0. The solutions are x = 0, π, 2π, ...

   For 1 - sin^2x = 0, sin^2x = 1. The solutions are x = π/2, 3π/2, 5π/2, ...

So the solutions to the equation sin3x + sinx = 0 are x = 0, π, 2π, π/2, 3π/2, 5π/2, ...