Question

For the principal value, evaluate the following:

`sin^-1(-sqrt3/2)-2sec^-1(2tan  pi/6)`

Answer 1

`sin^-1(-sqrt3/2)-2sec^-1(2tan  pi/6)=-sin^-1(sqrt3/2)-2sec^-1(2xx1/sqrt3)`

`=-sin^-1(sqrt3/2)-2sec^-1(2/sqrt3)`

`=-sin^-1(sin  pi/3)-2sec^-1(sec  pi/6)`

`=-pi/3-pi/3`

`=-(2pi)/3`