Simplify: 18 sin3x cos3x

[Baron]

Simplify: 18 sin3x cos3x
a) 18 sin 6x
b) 9 sin 6x
c) 6 sin 9x
d) 6 sin 3x

The answer is apparently B. How? Please don't use calculus or any triple angle identities. If possible please use only double angle identities and sum and difference formulas

My work:
18 sin(2x+x) * cos(2x + x)

18*sin 2x cos x + cos 2x sin x * cos 2x cos x - sin 2x sin x

And when I use the identities sin(2x) = 2sin x cos x ... that gets me nowhere.

 

[tkhunny]

No, really, the very last thing you said was the most useful. Just use it backwards.

What if I write it this way?

\(\displaystyle \sin(2A) = 2\cdot\sin(A)\cos(A)\)

...and then suggested that A = 3x?