Proving

Chapter 8 Class 10 Introduction to Trignometry
Concept wise

Transcript

Example 4 In a right triangle ABC, right-angled at B, if tan A = 1, then verify that 2 sin A cos A = 1. In a right angle triangle ABC tan A = 1 (𝑠𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒 𝐴)/(𝑆𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒 𝐴) = 1 𝐵𝐶/𝐴𝐵 = 1 AB = BC Let AB = BC = k Where k is a positive number. Finding AC by pythagoras theorem (Hypotenuse)2 = (Height)2 + (Base)2 AC2 = AB2 + BC2 Putting AB = BC = k AC2 = k2 + k2 AC2 = 2k2 AC = √2𝑘2 AC = √𝟐 "k" Now, cos A = (𝑠𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑛𝑐𝑒𝑛𝑡 𝑎𝑛𝑔𝑙𝑒 𝐴)/𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 cos A = 𝐴𝐵/𝐴𝐶 cos A = 𝑘/(𝑘√2) cos A = 𝟏/√𝟐 sin A = (𝑠𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑎𝑛𝑔𝑙𝑒 𝐴)/𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 sin A = 𝐵𝐶/𝐴𝐶 sin A = 𝑘/(𝑘√2) sin = 𝟏/√𝟐 We have to find 2 sin A cos A Substituting the value of sin A and cos A = 2 ×1/√2×1/√2 = 𝟐/(√𝟐 × √𝟐) = 2/(√2 )^2 = 2/2 = 1

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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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.