How do you verify $cos^2(2alpha) - sin^2(2alpha)=cos(4alpha)$ ?

Question

4113 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-17T01:35:08

See below

LHS = left hand side, RHS = right hand side

LHS $=(1-sin^2 2alpha) - sin ^2 2alpha$

$=1-2 sin^2 2alpha$

$=cos2(2alpha)$

$=cos 4 alpha$

$=RHS$

How do you verify cos^2(2alpha) - sin^2(2alpha)=cos(4alpha)cos^2(2alpha) - sin^2(2alpha)=cos(4alpha)?