How do you calculate #Cos^-1(5/13) - Cos^-1(8/17)#?
With a calculator. A TI-8# can do this with 2nd+COS. 13 and 17 are prime numbers, so 5/13 and 8/17 will give you irrational values. This isn't easily doable enough by hand to be something you need to do by hand.
Another way would be to let
From the identity
We can obtain that,