# Math Help - Simplifying trig functions

1. ## Simplifying trig functions

I'm sure that I'm missing an identity here, but how do I get from:

-4cos(t)cos(2t)-2sin(t)sin(2t)

to

-4cos3(t)

Thanks for any help.

2. ## Re: Simplifying trig functions

Originally Posted by MajMinor
I'm sure that I'm missing an identity here, but how do I get from:

-4cos(t)cos(2t)-2sin(t)sin(2t)

to

-4cos3(t)

Thanks for any help.
Use the product to sum identities to get

$-4\left( \frac{\cos(3t)+\cos(t)}{2} \right)-2\left( \frac{\cos(t)-\cos(3t)}{2} \right) = -\cos(3t)-3\cos(t)$

by the triple angle forumla you get the desired result

$-4\cos^3(t)$

3. ## Re: Simplifying trig functions

Thanks for the help.