Ex 8.1, 8 - If 3 cot A = 4, check (1 - tan2 A)/(1 + tan2 A) - Ex 8.1

  1. Chapter 8 Class 10 Introduction to Trignometry
  2. Serial order wise
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Ex 8.1, 8 If 3 cot A = 4, check whether ((1 โˆ’ ๐‘ก๐‘Ž๐‘›2๐ด))/((1 + ๐‘ก๐‘Ž๐‘›2๐ด))= cos2 A โ€“ sin2A or not. 3 cot A = 4 cot A = 4/3 So, tan A = 1/cotโก๐ด tan A = 1/((4/3) ) tan A = 3/4 (๐‘†๐‘–๐‘‘๐‘’ ๐‘œ๐‘๐‘๐‘œ๐‘ ๐‘–๐‘ก๐‘’ โˆ ๐ด)/(๐‘†๐‘–๐‘‘๐‘’ ๐‘Ž๐‘‘๐‘—๐‘Ž๐‘๐‘’๐‘›๐‘ก โˆ ๐ด) = 3/4 ๐ต๐ถ/๐ด๐ต = 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 = โˆš(25"x2" ) AC = 5x sin ๐ด = (๐‘ ๐‘–๐‘‘๐‘’ ๐‘œ๐‘๐‘๐‘œ๐‘ ๐‘–๐‘ก๐‘’ ๐‘ก๐‘œ โˆ ๐ด)/๐ป๐‘ฆ๐‘๐‘œ๐‘ก๐‘’๐‘›๐‘ข๐‘ ๐‘’ = ๐ต๐ถ/๐ด๐ถ = 3๐‘ฅ/5๐‘ฅ = 3/5 Similarly, cos A = (๐‘ ๐‘–๐‘‘๐‘’ ๐‘Ž๐‘‘๐‘—๐‘Ž๐‘๐‘’๐‘›๐‘ก ๐‘ก๐‘œ ๐ด)/๐ป๐‘ฆ๐‘๐‘œ๐‘ก๐‘’๐‘›๐‘ข๐‘ ๐‘’ = ๐ด๐ต/๐ด๐ถ = 4๐‘ฅ/5๐‘ฅ = 4/5 We have to check whether , (1 โˆ’ ๐‘ก๐‘Ž๐‘›2 ๐ด)/(1 + ๐‘ก๐‘Ž๐‘›2 ๐ด ) = cos2 A โ€“ sin2 A

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