Book: RD Sharma - Mathematics (Volume 1)
Chapter: 4. Inverse Trigonometric Functions
Subject: Maths - Class 12th
Q. No. 3 of Exercise 4.6
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3
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
= 
= 
