# Math Help - Trig Equality

1. ## Trig Equality

When doing some trig practice in my free time, I came across the problem if $\sin 2\alpha = \frac{1}{7}$, find $\sin^4 \alpha + \cos^4 \alpha$.

I did a little research online, and I found that $\sin^4 \alpha + \cos^4 \alpha = \frac{1}{4}(\cos 4\alpha + 3)$, which simplified the problem greatly, and I was able to find that the answer is $\frac{97}{98}$. Nevertheless, I feel that there is probably a "cleaner" way of doing this that does not require knowing the above equivalence.

Does anyone have any suggestions on how to attempt this question? Thanks!

2. ## Re: Trig Equality

Use following facts :

$\sin^4 \alpha + \cos^4 \alpha=(\sin^2 \alpha+\cos^2 \alpha)^2-2\sin^2 \alpha \cdot \cos^2 \alpha$

$\sin 2 \alpha=2\sin \alpha \cdot \cos \alpha$

3. ## Re: Trig Equality

Thank you very much! That made it so easy to do!