Question

How do you evaluate `arcsin(-1/2) + arctan(1) +arccos(-1/2)`?

Answer 1

Restricting to principal values, `(5pi)/12`.

Explanation:

The principal values sum is

`-pi/6 + pi/4 + (2pi)/3`

`=(5pi)/12`.

The general values sum is

`( l pi + (-1)^l(pi/6) ) + ( m pi + (-1)^m(pi/4) ) + ( 2 n pi +-(2pi)/3 ), l, m, n = 0, +-1, +-2, +-3, ...`