Example 7 - Show that tan-1 x + tan-1 2x/(1-x2) - Inverse

Example 7 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 2

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

Transcript

Example 7 Show that tan-1 ๐‘ฅ + tan-1 2๐‘ฅ/(1 โˆ’๐‘ฅ2) = tan-1 (3๐‘ฅ โˆ’ ๐‘ฅ3)/(1 โˆ’ 3๐‘ฅ2) Solving L.H.S tan-1 ๐‘ฅ + tan-1 2๐‘ฅ/(1 โˆ’ ๐‘ฅ2) = tan-1 (๐‘ฅ + 2๐‘ฅ/(1 โˆ’ ๐‘ฅ2))/(1โˆ’ ๐‘ฅ ร— 2๐‘ฅ/(1 โˆ’ ๐‘ฅ2)) = tan-1 ((๐‘ฅ(1 โˆ’ ๐‘ฅ2) + 2๐‘ฅ)/(1 โˆ’ ๐‘ฅ2))/(ใ€–(1 โˆ’ ๐‘ฅ2) โˆ’ 2๐‘ฅใ€—^2/(1 โˆ’ ๐‘ฅ2)) We know that tan-1 x + tan-1 y = tan-1 ((๐’™+๐’š )/(๐Ÿ โˆ’๐’™๐’š)) Replacing x by x and y by 2๐‘ฅ/(1 โˆ’ ๐‘ฅ2) = tan-1 ((๐‘ฅ โˆ’ ๐‘ฅ3 + 2๐‘ฅ)/(1 โˆ’ ๐‘ฅ2))/(ใ€–1 โˆ’ ๐‘ฅ2โˆ’ 2๐‘ฅใ€—^2/(1 โˆ’ ๐‘ฅ2)) = tan-1 ((3๐‘ฅ โˆ’ ๐‘ฅ3)/(1 โˆ’ ๐‘ฅ2))/(ใ€–1 โˆ’ 3๐‘ฅใ€—^2/(1 โˆ’ ๐‘ฅ2)) = tan-1 (3๐‘ฅ โˆ’ ๐‘ฅ3)/(1 โˆ’ ๐‘ฅ2) ร— (1 โˆ’ ๐‘ฅ2)/ใ€–1 โˆ’ 3๐‘ฅใ€—^2 = tan-1 (3๐‘ฅ โˆ’ ๐‘ฅ3)/ใ€–1 โˆ’ 3๐‘ฅใ€—^2 = R.H.S Thus L.H.S = R.H.S Hence proved

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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.