Evaluate each of the following:

Let tan^–1() = y

⇒ tan y =

= – tan

= tan

∴ The principal value of tan^–1() is …(1)

Let cot^–1() = z

⇒ cot z =

= – cot

= cot

= cot

The range of principal value of cot^–1is (0, π)

and cot

∴ The principal value of cot^–1() is …(2)

sin = –1

∴ tan^–1(–1)

Let tan^–1(–1) = w

⇒ tan w = –1

= – tan = 1

= tan

∴ The principal value of tan^–1(–1) is …(3)

From(1),(2) and (3) we get

=

=