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  1. Chapter 2 Class 12 Inverse Trigonometric Functions
  2. Serial order wise

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 value 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
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.