Question

For the principal value, evaluate the following:

`sin^-1(-sqrt3/2)+\text{cosec}^-1(-2/sqrt3)`

Answer 1

`sin^-1(-sqrt3/2)+cosec^-1(-2/sqrt3)=-sin^-1(sqrt3/2)+cosec^-1(-2/sqrt3)`

`=-sin^-1(sin  pi/3)+cosec^-1[cosec(-pi/3)]`

`=-pi/3-pi/3`

`=-(2pi)/3`