Prove that the following equation is an identity.(sin(4t)/8)=(1/2)(sin(t)co s(t)-2sin(^3)cos(t))

Given identity:     for the left-hand sideuse double angle identity  with      use sine double angle identity again on sin(2t)this gets us that 1/2 fraction that the right-hand side has    we can use a cosine double angle identity. we have the following possible forms to choose from:     because the right-hand side does not have any other powers of cosine and only a sine expression raised to a power of three, use the      form for      distribute only the sine and cosine and we get