# Math Help - Half angle formula problem

1. ## Half angle formula problem

Having trouble applying half angle formula in this question,

Any hints would be great

sin^4Θ=3/8 - 1/2cos(2Θ) + 1/8 cos(4Θ) is a solution for any angle Θ

use half angle formula and cos^2(2Θ)=1/2 cos(4Θ) +1/2

thanks

p.s just moved this, posted it in geometry by accident

2. $\sin^4\theta=(\sin^2\theta)^2=\left(\frac{1-\cos 2\theta}{2}\right)^2=$

$=\frac{1}{4}(1-2\cos 2\theta+\cos^2 2\theta)=$

$=\frac{1}{4}\left(1-2\cos 2\theta+\frac{1+\cos 4\theta}{2}\right)=$

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

$=\frac{3}{8}-\frac{1}{2}\cos 2\theta+\frac{1}{8}\cos 4\theta$