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Ex 2.2, 6 - Simplify: tan-1 1/root (x2-1) - Class 12 Inverse - Not clear how to approach

  1. Chapter 2 Class 12 Inverse Trigonometric Functions
  2. Serial order wise
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Ex 2.2, 6 Write the function in the simplest form: tan-1 1/√(𝑥^2−1), |x| > 1 tan-1 (1/√(𝑥^2 − 1)) Putting x = sec θ = tan-1 (1/√(sec^2⁡θ − 1)) = tan-1 (1/√(〖(1 + tan^2〗⁡θ ) − 1)) = tan-1 (1/√(〖1 −1 + tan^2〗⁡θ )) = tan-1 (1/√(tan^2⁡θ )) = tan-1 (1/tan⁡θ ) = tan-1 (cot θ) = tan-1 tan (90 – θ) = 90 – θ = 𝜋/2 – θ We assumed x = sec θ sec θ = x θ = sec-1 x Hence tan-1 (1/√(𝑥^2−1)) = 𝜋/2 – θ = 𝜋/2 – sec-1 x

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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