# How can I simplify sin(3x)cos(3x) using a multiple angle formula?

## I need to rewrite $\sin 3 x \cos 3 x$ using a multiple angle formula.

Oct 23, 2016

This can be simplified as $\frac{\sin 6 x}{2}$

#### Explanation:

According to the double angle formula:

## $\sin 2 x = 2 \sin x \cos x$

From this we can say that: $\sin x \cos x = \frac{\sin 2 x}{2}$ or more generally:

$\sin n x \cos n x = \frac{\sin 2 n x}{2}$.

If we apply this rule to the given example we get:

$\sin 3 x o s 3 x = \frac{\sin 6 x}{2}$