Question

Simplify the expression by using a double-angle formula 1-2sin^2(3theta)

Answer 1

We know that:

$\cos(2x)=1-2\sin^2(x)$

Here $x=3\theta$ so:

$1-2\sin^2(3\theta)=\cos(2\cdot3\theta)=\cos(6\theta)$