I'll just throw the three questions out first:

tan^-1(1/sqrt(3))

sec^-1(2)

Both of those I need the exact answer

cos(2tan^-1x)

That I need simplified.

(this is all supposed to be revision, by the way)

For the first two we were told to draw a triangle, and put the values there to make solving the problem geometrically simple, but I was never really taught the difference between cosine and arcsine (or any of the other ones, for that matter), so I'm not sure how to proceed

The last one I just don't know how to do.