Check sibling questions

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

Ex 8.1, 8 - Chapter 8 Class 10 Introduction to Trignometry - Part 2
Ex 8.1, 8 - Chapter 8 Class 10 Introduction to Trignometry - Part 3
Ex 8.1, 8 - Chapter 8 Class 10 Introduction to Trignometry - Part 4

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Transcript

Ex 8.1, 8 If 3 cot A = 4, check whether ((1 − 𝑡𝑎𝑛2𝐴))/((1 + 𝑡𝑎𝑛2𝐴))= cos2 A – sin2A or not. 3 cot A = 4 cot A = 4/3 So, tan A = 1/cot⁡𝐴 tan A = 1/((4/3) ) tan A = 3/4 (𝑆𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 ∠𝐴)/(𝑆𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 ∠𝐴) = 3/4 𝐵𝐶/𝐴𝐵 = 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 = √(25"x2" ) AC = 5x sin 𝐴 = (𝑠𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 ∠𝐴)/𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 = 𝐵𝐶/𝐴𝐶 = 3𝑥/5𝑥 = 3/5 Similarly, cos A = (𝑠𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 𝐴)/𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 = 𝐴𝐵/𝐴𝐶 = 4𝑥/5𝑥 = 4/5 We have to check whether , (1 − 𝑡𝑎𝑛2 𝐴)/(1 + 𝑡𝑎𝑛2 𝐴 ) = cos2 A – sin2 A

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.