Question

Express $\cos 4\theta$ in terms of $\cos \theta$.

Answer 1

Using $\cos 2\theta =2{\cos }^2\theta -1$

We have,

$\cos 4\theta$

$=2{\cos }^{2}2\theta -1$

$=2(2{\cos }^2\theta -1{)}^2-1$

$=8{\cos }^4\theta -4{\cos }^2\theta +1$.