Answer
See the steps.
Work Step by Step
$RHS =\dfrac{1}{4}+ \dfrac{\cos{2\theta}}{2}+ \dfrac{\cos^2{2\theta}}{4} = (\dfrac{\cos{2\theta}}{2}+ \dfrac{1}{2})^2$
$RHS = (\dfrac{\cos{2\theta}+1}{2})^2 = (\cos^2{\theta})^2 = \cos^4{\theta} = LHS$
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.