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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.

You can download the question paper hereΒ  https://www.teachoo.com/cbse/sample-papers/

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


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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.