Solve sin^3x=sinx

Question

I'm having some trouble solving this problem, can someone please explain the steps for me...

Answer 1

sin³x - sinx = 0

 

sinx(sin²x - 1) = 0

 

sinx(sinx - 1)(sinx + 1) = 0

 

sinx = 0, sinx = 1, or sinx = -1

 

Solutions in the interval [0, 2π] are 0, π/2, π, 3π/2, 2π