Last updated at Aug. 5, 2021 by Teachoo

Transcript

Ex 8.1, 8 If 3 cot A = 4, check whether ((1 โ ๐ก๐๐2๐ด))/((1 + ๐ก๐๐2๐ด))= cos2 A โ sin2A or not. 3 cot A = 4 cot A = 4/3 So, tan A = 1/cotโก๐ด tan A = 1/((4/3) ) tan A = 3/4 (๐๐๐๐ ๐๐๐๐๐ ๐๐ก๐ โ ๐ด)/(๐๐๐๐ ๐๐๐๐๐๐๐๐ก โ ๐ด) = 3/4 ๐ต๐ถ/๐ด๐ต = 3/4 Let BC = 3x & AB = 4x We find AC using Pythagoras theorem (Hypotenuse)2 = (Height)2 + (Base)2 (AC)2 = (AB)2 + (BC)2 (AC)2 = (4x)2 + (ex)2 (AC)2 = 16x2 + 9x2 (AC)2 = 25x2 AC = โ(25"x2" ) AC = 5x sin ๐ด = (๐ ๐๐๐ ๐๐๐๐๐ ๐๐ก๐ ๐ก๐ โ ๐ด)/๐ป๐ฆ๐๐๐ก๐๐๐ข๐ ๐ = ๐ต๐ถ/๐ด๐ถ = 3๐ฅ/5๐ฅ = 3/5 Similarly, cos A = (๐ ๐๐๐ ๐๐๐๐๐๐๐๐ก ๐ก๐ ๐ด)/๐ป๐ฆ๐๐๐ก๐๐๐ข๐ ๐ = ๐ด๐ต/๐ด๐ถ = 4๐ฅ/5๐ฅ = 4/5 We have to check whether , (1 โ ๐ก๐๐2 ๐ด)/(1 + ๐ก๐๐2 ๐ด ) = cos2 A โ sin2 A

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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.