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

Question

I need to rewrite #sin3xcos3x# using a multiple angle formula.

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Answer 1 · 2016-10-23T17:31:57

This can be simplified as #(sin6x)/2#

According to the double angle formula:

From this we can say that: #sinxcosx=(sin2x)/2# or more generally:

#sinnxcosnx=(sin2nx)/2#.

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

#sin3xos3x=(sin6x)/2#