Question

can someone help in xpanding this
=cos4θ

Answer 1

\[\cos(2\theta+2\theta) = \cos(2\theta)\cos(2\theta)-\sin(2\theta)\sin(2\theta)\]\[= \cos^2(2\theta) - \sin^2(2\theta)\]

Now, \[\sin^2(2\theta)+\cos^2(2\theta) = 1\]

So, \[\cos (4\theta)\ = cos^2(2\theta) - (1-\cos^2(2\theta)) = 2\cos^2(2\theta-1)\]