Question 3 - Ex 2.2 - Chapter 2 Class 12 Inverse Trigonometric Functions

Last updated at Dec. 16, 2024 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

Question 3 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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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