Example 6 - Class 12

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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^2⁡θ − 1)) = cot-1 (1/√(〖(1 + tan^2〗⁡θ ) − 1)) = cot-1 (1/√(〖1 −1 + tan^2〗⁡θ )) = cot-1 (1/√(tan^2⁡θ )) = cot-1 (1/tan⁡θ ) = 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