Find the value of: `cos^(-1)(1/2)+2sin^(-1)(1/2)`

Explanation

We know that the ranges of principal values of `cos^(-1)` and `sin^(-1)` are `[0,pi]` and `[-pi/2, pi/2]` respectively.
Let `cos^(-1)(1/2)=theta_(1)`. Then,
`costheta_(1)=1/2=cospi/2 rArr theta_(1)=pi/3 in [0,po]`.
Let `sin^(-1)(1/2)=theta`. Then,
`sintheta_(2)=1/2=sinpi/2 rArr theta_(2)=pi/6 in [-pi/2, pi/2]`.
`therefore cos^(-1)(1/2) + 2sin^(-1)(1/2)=pi/3+(2 xx pi/6) = (pi/3+pi/3)=(2pi)/3`.