Find the principal value of the following
(i) `sin^(-1).(1)/(2)`
(ii) `tan ^(-1).(1)/sqrt(3)`
(iii) `cot ^(-1)(-sqrt3)`

Explanation

(i) ` sin^(-1).(1)/(2) = sin ^(-1) (sin .(pi)/(6)) = (pi)/(6)`
(ii) `tan^(-1).(1)/(sqrt(3)) = tan^(-1)(tan .(pi)/(6))=(pi)/(6)`
(iii) `cot^(-1)(-sqrt(3)) = pi - cot^(-1) (sqrt(3))`
` = pi cot^(-1)(cot.(pi)/(6))`
` = pi -(pi)/(6) = (5pi)/(6)`