Ex 2.2, 6 - Chapter 2 Class 12 Inverse Trigonometric Functions (Term 1)

Last updated at March 30, 2023 by Teachoo

Ex 2.2, 6 - Simplify: tan-1 1/root (x2-1) - Class 12 Inverse

Ex 2.2, 6 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 2

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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〗^𝟐⁡𝜽 − 1)) = tan−1 (1/√(〖(𝟏 + 〖𝒕𝒂𝒏〗^𝟐〗⁡𝜽 ) − 1)) = tan−1 (1/√(tan^2⁡θ )) = tan−1 (1/tan⁡θ ) We write 1/√(𝑥^2 − 1) in form of tan Whenever there is √(𝑥^2−1) , we put x = sec 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, our equation becomes tan-1 (1/√(𝑥^2−1)) = 𝜋/2 – θ = 𝝅/𝟐 – sec−1 x (cot θ = tan (90 – θ) )

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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