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Question 6 - CBSE Class 10 Sample Paper for 2018 Boards - Solutions of Sample Papers for Class 10 Boards

Last updated at Dec. 16, 2024 by Teachoo

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/

Transcript

Question 6 If cos A = 2/5 , find the value of 4 + 4 tan2 A Given cos A = 2/5 (𝑆𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 ∠𝐴)/𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 = 2/5 𝐴𝐵/𝐴𝐶=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 = √(21𝑥^2 ) BC = √21 𝑥 Now, tan A = (𝑆𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 ∠𝐴)/(𝑆𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 ∠𝐴) tan A = 𝐵𝐶/𝐴𝐵 tan A = (√21 𝑥)/2𝑥 tan A = √21/2 Thus, 4 + 4 tan2 A = 4 + 4 (√21/2)^2 = 4 + 4 × 21/4 = 4 + 21 = 25
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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 and Computer Science at Teachoo