# Confused, has to be something simple.

• Oct 18th 2009, 12:44 PM
Djaevel
Confused, has to be something simple.
Must prove using different identities that the left side equals the right side, meaning you don't change the right side at ALL

I tried using double angle identities after factoring it (Difference of squares right?) But it didnt seem to work?

Any ideas?

$Cos^2 2u - Sin^2 2u = 2Cos^2 2u -1$
• Oct 18th 2009, 12:48 PM
skeeter
Quote:

Originally Posted by Djaevel
Must prove using different identities that the left side equals the right side, meaning you don't change the right side at ALL

I tried using double angle identities after factoring it (Difference of squares right?) But it didnt seem to work?

Any ideas?

$Cos^2 2u - Sin^2 2u = 2Cos^2 2u -1$

on the left side, change $\sin^2(2u)$ to $[1 - cos^2(2u)]$
• Oct 18th 2009, 12:49 PM
Quote:

Originally Posted by Djaevel
Must prove using different identities that the left side equals the right side, meaning you don't change the right side at ALL

I tried using double angle identities after factoring it (Difference of squares right?) But it didnt seem to work?

Any ideas?

$Cos^2 2u - Sin^2 2u = 2Cos^2 2u -1$

This is just the composite angle formula for the cosine of twice an angle. Don't let the $2u$ confuse you. They are using it as the argument on all the functions, so it's equivalent to just x. So this is actually very simple. The function:

$sin^2(2u)=1-cos^2(2u)$

Can be substituted into the left side of the euqation, to obtain the right side.
• Oct 18th 2009, 12:52 PM
Djaevel
Haha thanks guys :)