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Last updated at Feb. 13, 2020 by Teachoo

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Example 6 Write cot−1 (1/√(𝑥^2 − 1)), |𝑥| > 1 in the simplest form. cot-1 (1/√(𝑥^2 − 1)) Putting x = sec θ = cot−1 (1/√(sec^2θ − 1)) = cot−1 (1/√(〖(1 + tan^2〗θ ) − 1)) = cot−1 (1/√(〖1 − 1 + tan^2〗θ )) = cot−1 (1/√(tan^2θ )) We write 1/√(𝑥^2 − 1) in form of cot Whenever there is √(𝑥^2−1) , we put x = sec θ (sec2 θ = 1 + tan2 θ) = cot−1 (1/tanθ ) = cot−1 (cot θ) = θ We assumed x = sec θ sec θ = x θ = sec−1 x Hence, cot−1 (1/√(𝑥^2−1)) = θ cot−1 (1/√(𝑥^2−1)) = sec−1 x (1/𝑡𝑎𝑛𝜃 " = cot θ" )

Chapter 2 Class 12 Inverse Trigonometric Functions

Serial order wise

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.