Question

Find the principal value of the following:

`tan^-1(cos  pi/2)`

Answer 1

Let `tan^-1(cos  pi/2)=y`

Then,

`tany=cospi/2`

We know that the range of the principal value branch is `(-pi/2,pi/2)`

Thus,

`tany=cos  pi/2=0=tan(0)`

`=>y=0in(-pi/2,pi/2)`

Hence, the principal value of `tan^-1(cos  pi/2)`  is 0.