Question

Find the principal value of the following:

`cot^-1(tan  (3pi)/4)`

Answer 1

Let `cot^-1(tan  (3pi)/4) = y`

Then,

`coty=tan  (3pi)/4`

We know that the range of the principal value branch is (0, π).

Thus,

`coty=tan  (3pi)/4=-1=cot((3pi)/4)`

`=>y=(3pi)/4in(0,pi)`

Hence, the principal value of `cot^-1(tan  (3pi)/4)    is    (3pi)/4.`