# Thread: Expressing sin(2x)sin(x) as a sum or difference of sin/cos terms

1. ## Expressing sin(2x)sin(x) as a sum or difference of sin/cos terms

This site is excellent its really helping me understand the problems I am having.

Anyway my latest problem is:

Express sin(2x)sin(x) as a sum or difference of sin/cos terms.

Can anyone help me?

2. Originally Posted by JQ2009
This site is excellent its really helping me understand the problems I am having.

Anyway my latest problem is:

Express sin(2x)sin(x) as a sum or difference of sin/cos terms.

Can anyone help me?
HI

$\displaystyle \sin 2x\sin x=(2\sin x\cos x)\sin x$

$\displaystyle =2\sin^2 x\cos x$

$\displaystyle =2(1-\cos^2 x)(\cos x)$

$\displaystyle =2\cos x-2\cos^3 x$

3. Express sin(2x)sin(x) as a sum or difference of sin/cos terms.
$\displaystyle as\ we\ know\ that\ \boxed{2 \sin C \sin D = \cos(C-D) - \cos(C+D) }$

$\displaystyle therefore\ \sin 2x \sin x = \frac{1}{2} \{ \cos(2x-x) - \cos(2x+x) \}$
$\displaystyle \sin 2x \sin x = \frac{1}{2} \{ \cos x - \cos 3x \}$