Check sibling questions

Ex 2.2, 4 - Prove 2tan-1 1/2 + tan-1 1/7 = tan-1 31/17 - Ex 2.2

Ex 2.2, 4 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 2
Ex 2.2, 4 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 3

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Question 2 Prove 2tanโˆ’1 1/2 + tanโˆ’1 1/7 = tanโˆ’1 31/17 Value of 2tanโˆ’1 ๐Ÿ/๐Ÿ We know that 2tanโˆ’1x = tanโˆ’1 ((๐Ÿ๐ฑ )/( ๐Ÿ โˆ’ ๐ฑ^๐Ÿ )) Replacing x with 1/2 2tanโˆ’1 1/2 = tanโˆ’1 (2 ร— 1/2)/(1 โˆ’ (1/2)2) = tanโˆ’1 (1/(1 โˆ’ 1/4)) = tanโˆ’1 (1/((4 โˆ’ 1)/4)) = tanโˆ’1 (1/(3/4)) = tanโˆ’1 (๐Ÿ’/๐Ÿ‘) Solving L.H.S. 2tanโˆ’1 1/2 + tanโˆ’1 1/7 Putting value of 2tanโˆ’1 1/2 = tanโˆ’1 4/3 + tanโˆ’1 1/7 = tanโˆ’1 (1/(1 โˆ’ 1/4)) = tanโˆ’1 (1/((4 โˆ’ 1)/4)) = tanโˆ’1 (1/(3/4)) = tanโˆ’1 (๐Ÿ’/๐Ÿ‘) Solving L.H.S. 2tanโˆ’1 1/2 + tanโˆ’1 1/7 Putting value of 2tanโˆ’1 1/2 = tanโˆ’1 4/3 + tanโˆ’1 1/7 Using tanโˆ’1x + tanโˆ’1y = tanโˆ’1 ((๐’™ + ๐’š )/( ๐Ÿโˆ’ ๐’™๐’š)) Replacing x by 4/3 and y by 1/(7 )= tanโˆ’1 ((๐Ÿ’/๐Ÿ‘ + ๐Ÿ/๐Ÿ• )/( ๐Ÿโˆ’ ๐Ÿ’/๐Ÿ‘ ร— ๐Ÿ/๐Ÿ•)) = tanโˆ’1 (((4 ร— 7 +3 ร— 1 )/( 7 ร— 3) )/( (7 ร— 3 โˆ’ 4)/(7 ร— 3))) = tanโˆ’1 (((28 + 3 )/( 21) )/( ( 21 โˆ’ 4)/21)) = tanโˆ’1 ((31/( 21) )/(17/21)) = tanโˆ’1 (31/21ร—21/17) = tanโˆ’1 (๐Ÿ‘๐Ÿ/๐Ÿ๐Ÿ•) = R.H.S. Hence, L.H.S. = R.H.S. Hence Proved

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

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.