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 here  https://www.teachoo.com/cbse/sample-papers/

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Question 6 If cos A = 2/5 , find the value of 4 + 4 tan2 A Given cos A = 2/5 (๐‘†๐‘–๐‘‘๐‘’ ๐‘Ž๐‘‘๐‘—๐‘Ž๐‘๐‘’๐‘›๐‘ก ๐‘ก๐‘œ โˆ ๐ด)/๐ป๐‘ฆ๐‘๐‘œ๐‘ก๐‘’๐‘›๐‘ข๐‘ ๐‘’ = 2/5 ๐ด๐ต/๐ด๐ถ=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 โ€“ 4x2 (BC) 2 = 21x2 BC = โˆš(21๐‘ฅ^2 ) BC = โˆš21 ๐‘ฅ Now, tan A = (๐‘†๐‘–๐‘‘๐‘’ ๐‘œ๐‘๐‘๐‘œ๐‘ ๐‘–๐‘ก๐‘’ ๐‘ก๐‘œ โˆ ๐ด)/(๐‘†๐‘–๐‘‘๐‘’ ๐‘Ž๐‘‘๐‘—๐‘Ž๐‘๐‘’๐‘›๐‘ก ๐‘ก๐‘œ โˆ ๐ด) tan A = ๐ต๐ถ/๐ด๐ต tan A = (โˆš21 ๐‘ฅ)/2๐‘ฅ tan A = โˆš21/2 Thus, 4 + 4 tan2 A = 4 + 4 (โˆš21/2)^2 = 4 + 4 ร— 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 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.