1. ## complex no.

p302 q13
prove that $16cos^4x sin x = sin 5x +3sin3x+2sinx$
my working:
let
$z = cos x + i sin x$
$z + 1/z = cos x$
$z - 1/z = i sin x$
i can only prove $16cos^4x sin x = 16 ( sin 5x + 3 sin 3x + 2sinx) 2i$
what's wrong?
thanks

2. Yop,

Originally Posted by afeasfaerw23231233
p302 q13
prove that $16cos^4x sin x = sin 5x +3sin3x+2sinx$
my working:
let
$z = cos x + i sin x$
$z + 1/z ={\color{red}2} cos x$
$z - 1/z ={\color{red}2} i sin x$
i can only prove $16cos^4x sin x = 16 ( sin 5x + 3 sin 3x + 2sinx) 2i$
what's wrong?
thanks

Though I have no time at the moment to check if your method will yield the thing we want, because of i.. ^^'

3. Originally Posted by afeasfaerw23231233
p302 q13
prove that $16cos^4x sin x = sin 5x +3sin3x+2sinx$
my working:
let
$z = cos x + i sin x$
$z + 1/z = cos x$
$z - 1/z = i sin x$
i can only prove $16cos^4x sin x = 16 ( sin 5x + 3 sin 3x + 2sinx) 2i$
what's wrong?
thanks
$16\cos^4(x)\sin(x)=16\bigg(\frac{e^{ix}+e^{-ix}}{2}\bigg)^4\cdot\bigg(\frac{e^{ix}-e^{-ix}}{2}\bigg)$

That is generally how I start all of these problems. In this case it may not be as useful but it usually helps