Simplifying trig expressions

[csplinter]

This has long been one of my biggest issues using the HP Prime. I'll start with an example.

I do several calculations and end up with something like

81*sqrt(cos(v)^2 *sin(u)^4 +(cos(v)^2 -sin(v)^2)^2 *cos(u)^2 *sin(v)^2 +(cos(v)^2 -sin(v)^2)^2 *sin(u)^2

I know that this should simplify to 81*sin(u) or something like this.

I've tried simplify(), tcollect(), trigsin(), factor() and all kinds of random functions, but can't seem to get anything more readable. Why can't the HP Prime seem to recognize cos(x)^2+sin(x)^2 = 1?

I can manually make these observations if you could lead me in a direction that would eliminate the sqrt() and expand things such as (cos(v)^2 -sin(v)^2)^2 without messing things up further by adding a denominator or something.

Of course, if you can lead me to a solution that reduces the expression to something like 81*sin(u) I'll be your best friend. 3rd party apps and programs are fine, if need be.