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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
=
=