Question

sin3x=(sinx)(3-asin^2x)

Wow!
is that arcsin^2(x) ???

are we solving for x?
or is it proving the identity?

proving the identity
sin3x=(sinx)(3-sin^2x)

Your identity is wrong, it should say:

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

try this:
sin(3x) = sin(2x + x)
= sin2xcosx + cos2xsinx

keep replacing in terms of sinx, it comes out pretty smoothly.

proving the identity:
sin3x=(sinx)(3-4sin^2x)

proving the identity:
sin3x=(sinx)(3-4sin^2x)

Reiny gave you a hint:

in3x=(sinx)(3-4sin^2x)

try this:
sin(3x) = sin(2x + x)
= sin2xcosx + cos2xsinx


keep replacing in terms of sinx, it comes out pretty smoothly.