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Ex 2.2, 7 - Chapter 2 Class 12 Inverse Trignometry - tan-1

Ex 2.2, 7 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 2

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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

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.