Last updated at May 29, 2018 by Teachoo

Transcript

Ex 2.2, 4 Prove 2tan-1 1/2 + tan-1 1/7 = tan-1 31/17 First we calculate value of 2tan-1 ๐/๐ We know that 2tan-1x = tan-1 ((๐๐ฑ )/( ๐ โ ๐ฑ^๐ )) Replacing x with 1/2 2tan-1 1/2 = tan-1 (2 ร 1/2)/(1 โ (1/2)2) = tan-1 (1/(1 โ 1/4)) = tan-1 (1/((4 โ 1)/4)) = tan-1 (1/(3/4)) = tan-1 (4/3) Taking L.H.S. 2tan-1 1/2 + tan-1 1/7 Putting value of 2tan-1 1/2 = tan-1 4/3 + tan-1 1/7 = tan-1 ((4/3 + 1/7 )/( 1โ 4/3 ร 1/7)) = tan-1 (((4 ร 7 +3 ร 1 )/( 7 ร 3) )/( (7 ร 3 โ 4)/(7 ร 3))) = tan-1 (((28 + 3 )/( 21) )/( ( 21 โ 4)/21)) = tan-1 ((31/( 21) )/(17/21)) = tan-1 (31/21 ร 21/17)= tan-1 (31/17) = R.H.S. Hence, L.H.S. = R.H.S. Hence Proved

Chapter 2 Class 12 Inverse Trigonometric Functions

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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.