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

**JQ2009** · October 10th 2009, 06:40 AM

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?

**mathaddict** · October 10th 2009, 07:17 AM

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

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

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

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

$<br /> =2\cos x-2\cos^3 x<br />$

**ramiee2010** · October 10th 2009, 09:18 AM

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

$as\ we\ know\ that\ \boxed{2 \sin C \sin D = \cos(C-D) - \cos(C+D) }$

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

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