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

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

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Example 7 Show that tan-1 π‘₯ + tan-1 2π‘₯/(1 βˆ’π‘₯2) = tan-1 (3π‘₯ βˆ’ π‘₯3)/(1 βˆ’ 3π‘₯2) Solving L.H.S tan-1 π‘₯ + tan-1 2π‘₯/(1 βˆ’ π‘₯2) = tan-1 (π‘₯ + 2π‘₯/(1 βˆ’ π‘₯2))/(1βˆ’ π‘₯ Γ— 2π‘₯/(1 βˆ’ π‘₯2)) = tan-1 ((π‘₯(1 βˆ’ π‘₯2) + 2π‘₯)/(1 βˆ’ π‘₯2))/(γ€–(1 βˆ’ π‘₯2) βˆ’ 2π‘₯γ€—^2/(1 βˆ’ π‘₯2)) We know that tan-1 x + tan-1 y = tan-1 ((𝒙+π’š )/(𝟏 βˆ’π’™π’š)) Replacing x by x and y by 2π‘₯/(1 βˆ’ π‘₯2) = tan-1 ((π‘₯ βˆ’ π‘₯3 + 2π‘₯)/(1 βˆ’ π‘₯2))/(γ€–1 βˆ’ π‘₯2βˆ’ 2π‘₯γ€—^2/(1 βˆ’ π‘₯2)) = tan-1 ((3π‘₯ βˆ’ π‘₯3)/(1 βˆ’ π‘₯2))/(γ€–1 βˆ’ 3π‘₯γ€—^2/(1 βˆ’ π‘₯2)) = tan-1 (3π‘₯ βˆ’ π‘₯3)/(1 βˆ’ π‘₯2) Γ— (1 βˆ’ π‘₯2)/γ€–1 βˆ’ 3π‘₯γ€—^2 = tan-1 (3π‘₯ βˆ’ π‘₯3)/γ€–1 βˆ’ 3π‘₯γ€—^2 = R.H.S Thus L.H.S = R.H.S Hence proved

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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.