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^{–1}is (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

=

=

3