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If cos A = 2/5 , find the value of 4 + 4 tan 2 A

This is a question of CBSE Sample Paper - Class 10 - 2017/18.

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If cos A = 2/5 , find the value of 4 + 4 tan^2 A - Teachoo

Question 6 - CBSE Class 10 Sample Paper for 2018 Boards - Part 2
Question 6 - CBSE Class 10 Sample Paper for 2018 Boards - Part 3

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Transcript

Question 6 If cos A = 2/5 , find the value of 4 + 4 tan2 A Given cos A = 2/5 (𝑆𝑖𝑑𝑒 π‘Žπ‘‘π‘—π‘Žπ‘π‘’π‘›π‘‘ π‘‘π‘œ ∠𝐴)/π»π‘¦π‘π‘œπ‘‘π‘’π‘›π‘’π‘ π‘’ = 2/5 𝐴𝐡/𝐴𝐢=2/5 Let AB = 2x & AC = 5x Using Pythagoras theorem to find BC (Hypotenuse)2 = (Height)2 + (Base)2 AC2 = AB2 + BC2 (5x)2 = (2x)2 + (BC)2 (BC)2 = (5x)2 - (2x)2 (BC) 2 = 25x2 – 4x2 (BC) 2 = 21x2 BC = √(21π‘₯^2 ) BC = √21 π‘₯ Now, tan A = (𝑆𝑖𝑑𝑒 π‘œπ‘π‘π‘œπ‘ π‘–π‘‘π‘’ π‘‘π‘œ ∠𝐴)/(𝑆𝑖𝑑𝑒 π‘Žπ‘‘π‘—π‘Žπ‘π‘’π‘›π‘‘ π‘‘π‘œ ∠𝐴) tan A = 𝐡𝐢/𝐴𝐡 tan A = (√21 π‘₯)/2π‘₯ tan A = √21/2 Thus, 4 + 4 tan2 A = 4 + 4 (√21/2)^2 = 4 + 4 Γ— 21/4 = 4 + 21 = 25

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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.