Check sibling questions

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

This video is only available for Teachoo black users

Introducing your new favourite teacher - Teachoo Black, at only β‚Ή83 per month


Transcript

Ex 2.2, 6 Write the function in the simplest form: tanβˆ’1 1/√(π‘₯^2βˆ’1), |x| > 1 tanβˆ’1 (1/√(π‘₯^2 βˆ’ 1)) Putting x = sec ΞΈ = tanβˆ’1 (1/√(〖𝒔𝒆𝒄〗^𝟐⁑𝜽 βˆ’ 1)) = tanβˆ’1 (1/√(γ€–(𝟏 + 〖𝒕𝒂𝒏〗^πŸγ€—β‘πœ½ ) βˆ’ 1)) = tanβˆ’1 (1/√(tan^2⁑θ )) = tanβˆ’1 (1/tan⁑θ ) We write 1/√(π‘₯^2 βˆ’ 1) in form of tan Whenever there is √(π‘₯^2βˆ’1) , we put x = sec ΞΈ = tanβˆ’1 (cot ΞΈ) = tanβˆ’1 tan (90 – ΞΈ) = 90 – ΞΈ = 𝝅/𝟐 – ΞΈ We assumed x = sec ΞΈ sec ΞΈ = x ΞΈ = sec-1 x Hence, our equation becomes tan-1 (1/√(π‘₯^2βˆ’1)) = πœ‹/2 – ΞΈ = 𝝅/𝟐 – secβˆ’1 x (cot ΞΈ = tan (90 – ΞΈ) )

Davneet Singh's photo - Teacher, Engineer, Marketer

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.