Question

For the principal value, evaluate of the following:

`tan^-1{2sin(4cos^-1  sqrt3/2)}`

Answer 1

`tan^-1{2sin(4cos^-1  sqrt3/2)} = tan^-1{2sin[4cos^-1(cos  pi/6)]}`

`=tan^-1{2sin[4xxpi/6]}`

`=tan^-1(2sin  (2pi)/3)`

`=tan^-1[2xx(sqrt3/2)]`

`=tan^-1(sqrt3)`

`=tan^-1[tan(pi/3)]`

`= pi/3`