Simplifying $\sqrt\frac{\left(a^2\cos^2t+b^2\sin^2t\right)^3}{\left(b^2\cos^2t+a^2\sin^2t\right)^3}$ I am looking to simplify these term   [ I forgot the 3 :( ]

$$\sqrt\frac{\left(a^2\cos^2t+b^2\sin^2t\right)^3}{\left(b^2\cos^2t+a^2\sin^2t\right)^3}$$

where $a$ and $b$ are two non-negative reals.
(This is not homework. I am just trying to make my expression easy, but I didn't find a way.)
Thanks for your help.

For the radicand i have got
$$\frac{a^2 (-\cos (2 t))-a^2+b^2 \cos (2 t)-b^2}{a^2
   \cos (2 t)-a^2-b^2 \cos (2 t)-b^2}$$
