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Last updated at May 12, 2021 by Teachoo

Transcript

Ex 2.2, 7 Write the function in the simplest form: tan−1 (√((1 −〖 cos〗x)/(1 +〖 cos〗x ))), x < π Lets first calculate values of 1 – cos x & 1 + cos x We know that cos 2x = 1 – 2sin2x Replacing x by 𝑥/2 cos (2𝑥/2) = 1 – 2 sin2 𝑥/2 cos (x) = 1 – 2 sin2 𝑥/2 2 sin2 𝑥/2 = 1 – cos x 1 – cos x = 2 sin2 𝑥/2 We know that cos 2x = 2 cos2x – 1 Replacing x by 𝑥/2 cos (2𝑥/2) = 2 cos2 𝑥/2 – 1 cos x = 2 cos2 𝑥/2 – 1 1 + cos x = 2 cos2 𝑥/2 Now, tan-1 (√((1 −〖 cos〗x)/(1 +〖 cos〗x ))) = tan−1 (√((𝟐 𝐬𝐢𝐧𝟐 𝐱/𝟐 )/(𝟐 𝐜𝐨𝐬𝟐 𝐱/𝟐))) = tan−1 (√((sin2 x/2 )/(cos2 x/2))) = tan−1 (√(tan2〖 𝑥/2〗 )) = tan−1 (tan〖 𝑥/2〗 ) = 𝒙/𝟐

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

Ex 2.2, 4 Important Deleted for CBSE Board 2022 Exams

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Ex 2.2, 7 Important Deleted for CBSE Board 2022 Exams You are here

Ex 2.2, 8 Important Deleted for CBSE Board 2022 Exams

Ex 2.2, 9 Deleted for CBSE Board 2022 Exams

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, 14 Important Deleted for CBSE Board 2022 Exams

Ex 2.2, 15 Important Deleted for CBSE Board 2022 Exams

Ex 2.2, 16 Deleted for CBSE Board 2022 Exams

Ex 2.2, 17 Deleted for CBSE Board 2022 Exams

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.