How to simplify 1/(cos^4x+sin^4x)

[color_me]

1. The problem statement, all variables and given/known data
Simplify 1/(cos^4x+sin^4x)


2. Relevant equations
One can't apply cosine of a difference when the cosine is raised to a power, right?


3. The attempt at a solution
I tried using several trig identities, but it doesn't get any simpler.

Thank you for any help in advance!

[rock.freak667]

try replacing sin2x with 1-cos2x or the other way around.

[singular]

Try starting with the fundamental identity sin^{2}x + cos^{2}x=1. Square both sides and foil. This might get messy, but if you keep all your terms in order you will be in good shape. Next, look for your sin^{4}x and cos^{4}x values. You want to isolate them on one side and have the other terms on the other side. Now, you have to go to work with the other trig identities on the rest of the terms. I was able to do it product identities. In the end, you should have sin^{4}x+cos^{4}x=something. The last step is to plug this in to your original equation 1/sin^{4}x+cos^{4}x.

[color_me]

Thanks for the help! I figured it out.