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

2 Answers
Jun 21, 2018

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

Jun 21, 2018

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!