Last updated at May 12, 2021 by

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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

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

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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.