Last updated at May 12, 2021 by Teachoo

Transcript

Ex 2.2, 5 Write the function in the simplest form: tan−1 (√(1 + x^2 ) − 1)/x , x ≠ 0 tan−1 (√(1 + x^2 ) − 1)/x Putting x = tan 𝜃 = tan−1 ((√(𝟏 + 〖𝐭𝐚𝐧〗^𝟐 𝛉 )− 1)/(tan θ)) = tan−1 ((√(〖𝐬𝐞𝐜〗^𝟐 𝜽 ) − 1)/(tan θ)) = tan−1((secθ − 1)/(tan θ)) We write (√(1 + x^2 ) − 1)/x in form of tan Whenever there is √(1+ 𝑥^2 ) we put x = tan θ (sec2 θ = 1 + tan2 θ) = tan−1 ((1/cos𝜃 − 1)/(sin𝜃/cos𝜃 )) = tan−1 (((1 − cosθ)/cosθ )/(sin𝜃/cos𝜃 )) = tan−1 ((1 −〖 cos〗𝜃)/sin𝜃 ) Using sin 2θ = 2 sin θ cos θ Replacing θ with 𝜃/2 sin 2θ/2 = 2 sin θ/2 cos θ/2 sin θ = 2 sin 𝜃/2 cos 𝜃/2 Also, cos 2θ = 1 – 2 sin2 θ Replacing θ with 𝜃/2 cos 2(𝜃/2) = 1 − 2 sin2 𝜃/2 cos θ = 1 − 2 sin2 𝜃/2 2 sin2 𝜃/2 = 1 – cos θ 1 – cos θ = 2 sin2 𝜃/2 So, our equation becomes = tan−1 ((𝟐 𝒔𝒊𝒏𝟐 𝜽/𝟐)/(𝟐 〖𝐬𝐢𝐧 〗〖𝜽/𝟐〗 𝒄𝒐𝒔〖 𝜽/𝟐〗 )) = tan−1 (〖sin 〗〖𝜃/2〗/cos〖 𝜃/2〗 ) = tan−1 (𝑡𝑎𝑛 𝜃/2) = 𝛉/𝟐 We assumed that x = tan θ θ = tan-1x Hence, our equation becomes tan−1 (√(1 + x^2 ) − 1)/x = θ/2 = 𝟏/𝟐 tan-1x

Ex 2.2

Ex 2.2,1
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Ex 2.2, 2 Important Deleted for CBSE Board 2022 Exams

Ex 2.2, 3 Deleted for CBSE Board 2022 Exams

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Ex 2.2, 5 Important Deleted for CBSE Board 2022 Exams You are here

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Ex 2.2, 10 Important Deleted for CBSE Board 2022 Exams

Ex 2.2, 11 Deleted for CBSE Board 2022 Exams

Ex 2.2, 12 Important Deleted for CBSE Board 2022 Exams

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Ex 2.2, 18 Important Deleted for CBSE Board 2022 Exams

Ex 2.2, 19 (MCQ) Important Deleted for CBSE Board 2022 Exams

Ex 2.2, 20 (MCQ) Important Deleted for CBSE Board 2022 Exams

Ex 2.2, 21 (MCQ) Deleted for CBSE Board 2022 Exams

Chapter 2 Class 12 Inverse Trigonometric Functions (Term 1)

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.