p302 q13

prove that $\displaystyle 16cos^4x sin x = sin 5x +3sin3x+2sinx$

my working:

let

$\displaystyle z = cos x + i sin x$

$\displaystyle z + 1/z = cos x$

$\displaystyle z - 1/z = i sin x$

i can only prove $\displaystyle 16cos^4x sin x = 16 ( sin 5x + 3 sin 3x + 2sinx) 2i$

what's wrong?

thanks