sin3x−sinx=0

Answer 1

sin3x = sinx(2cos(2x)+1)
= sinx(2(1-2sin^2x)-1)
= sinx(1-4sin^2x)
= sinx - 4sin^3x

now you have sin^3(x) = 0

or, consider that sin(x)=0 at all multiples of pi.

Sin3x oscillates 3 times as fast, so it is also zero at multiples of pi.