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

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Answer 1 · 2016-07-28T03:56:27

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

The principal values sum is

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

$=(5pi)/12$ .

The general values sum is

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

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