# Thread: Double angle trig identity

1. ## Double angle trig identity

My teacher wrote this on the board
cos^2(2x) = (1+cos(6x))/2
Can someone please help me to understand this? I actually think I copied something down wrong. Thanks.

2. Originally Posted by pberardi
My teacher wrote this on the board
cos^2(2x) = (1+cos(6x))/2
Can someone please help me to understand this? I actually think I copied something down wrong. Thanks.
The power reduction formula for cosine is

$\cos^2x=\frac{1+\cos2x}2.$

So, $\cos^22x=\frac{1+\cos4x}2.$

3. So if I know for sure that the right hand side is (1+cos(6x))/2 then the left hand side would be cos^2(3x) ?? I am trying to figure out what exactly I copied down wrong. Thanks.

4. Originally Posted by pberardi
So if I know for sure that the right hand side is (1+cos(6x))/2 then the left hand side would be cos^2(3x) ??
Yes.