# Solving inverse trig functions

Supposing I need to solve a problem like: sec(arctan 2) or cos(2arcsin(5/13)), is there a method I could use that would not require a calculator? What I mean is that for an example like tan(arccos .5), the answer is "simple" because I know the arc cosine of .5 is pi/3 and then the tan of pi/3 is the squareroot of 3. But in a problem like the two above, how would I go about doing this where the numbers are more complicated and I want to do it by hand? Or is it impossible without the use of a calculator?