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Last updated at Feb. 13, 2020 by Teachoo
Transcript
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^2θ − 1)) = tan−1 (1/√(〖(1 + tan^2〗θ ) − 1)) = tan−1 (1/√(〖1 −1 + tan^2〗θ )) = tan−1 (1/√(tan^2θ )) We write 1/√(𝑥^2 − 1) in form of tan Whenever there is √(𝑥^2−1) , we put x = sec θ (sec2 θ = 1 + tan2 θ) = tan−1 (1/tanθ ) = 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 (1/tan𝜃 " = cot θ" ) (cot θ = tan (90 – θ) ) Hence, tan-1 (1/√(𝑥^2−1)) = 𝜋/2 – θ = 𝝅/𝟐 – sec−1 x
Ex 2.2
Ex 2.2, 2 Important Not in Syllabus - CBSE Exams 2021
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Ex 2.2, 6 Important Not in Syllabus - CBSE Exams 2021 You are here
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