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
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.
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