Question

How to simplify `cos^2 2theta-sin^2 2theta`?

Answer 1

`cos4theta`

Explanation:

`cos^2(2theta)-sin^2(2theta)`

=`cos2(2theta)`

=`cos4theta`

This is basically the double angle formula

Recall that `cos2x=cos^2x-sin^2x`

Now replace `x` with `2theta`

`cos2(2theta)=cos^2 (2theta)-sin^2 (2theta)`

`cos4theta=cos^2 2theta-sin^2 2theta`

Answer 2

This simplifies to `cos(4theta)`

Explanation:

Let `A=2theta`.

Then the expression becomes `cos^2A -sin^2A= cos(2A)`. Now reverse the substitution to see that the expression gives `cos(2(2theta))= cos(4theta)`

Hopefully this helps!