f[t_] = -4 + Sqrt[(-Sqrt + 2*Cos[t])^2 + Sin[t]^2] + Sqrt[(Sqrt + 2*Cos[t])^2 + Sin[t]^2]
The function above is identically 0 for all real values of t. However:
just spits back the original function.
I also tried TrigReduce, TrigExpand, etc, to no avail.
How do I make Mathematica simplify things like this?
For those interested: I'm playing w/ ellipses, and f[t] represents the sum of the distance from the focii minus the actual value of the sum of the distance from the focii. The more general case:
x[t_] = a*Cos[t] y[t_] = b*Sin[t] focus[a_,b_] = Sqrt[a^2-b^2] f[t_]=Sqrt[(x[t]-focus[a,b])^2 + y[t]^2] + Sqrt[(x[t]+focus[a,b])^2 + y[t]^2]
where f[t] is constant for real t when a >= b (probably when a < b too, but things get a bit complex in that case)