Question

Find the principal value of `tan^-1(1)+cos^-1(-1/2)+sin^-1(-1/root  2)`.

Answer 1

`tan^-1 (1) +cos^-1(-1/2)+sin^-1(-1/root  2)`

`= tan^-1 (tan  pi/4)+cos^-1(cos  (2pi)/3)+sin^-1(sin(-pi/4))`

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

`=(2pi)/3`