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


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 π‘œπ‘π‘π‘œπ‘ π‘–π‘‘π‘’ π‘‘π‘œ π‘Žπ‘›π‘”π‘™π‘’ 𝐴)/(𝑆𝑖𝑑𝑒 π‘Žπ‘‘π‘—π‘Žπ‘π‘’π‘›π‘‘ π‘‘π‘œ π‘Žπ‘›π‘”π‘™π‘’ 𝐴) = 1 𝐡𝐢/𝐴𝐡 = 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 = √2π‘˜2 AC = √𝟐 "k" Now, cos A = (𝑠𝑖𝑑𝑒 π‘Žπ‘‘π‘—π‘Žπ‘›π‘π‘’π‘›π‘‘ π‘Žπ‘›π‘”π‘™π‘’ 𝐴)/π»π‘¦π‘π‘œπ‘‘π‘’π‘›π‘’π‘ π‘’ cos A = 𝐴𝐡/𝐴𝐢 cos A = π‘˜/(π‘˜βˆš2) cos A = 𝟏/√𝟐 sin A = (𝑠𝑖𝑑𝑒 π‘œπ‘π‘π‘œπ‘ π‘–π‘‘π‘’ π‘Žπ‘›π‘”π‘™π‘’ 𝐴)/π»π‘¦π‘π‘œπ‘‘π‘’π‘›π‘’π‘ π‘’ sin A = 𝐡𝐢/𝐴𝐢 sin A = π‘˜/(π‘˜βˆš2) sin = 𝟏/√𝟐 We have to find 2 sin A cos A Substituting the value of sin A and cos A = 2 Γ—1/√2Γ—1/√2 = 𝟐/(√𝟐 Γ— √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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.