Question 6 If cos A = 2/5 , find the value of 4 + 4 tan2 A
Given cos A = 2/5
(๐๐๐๐ ๐๐๐๐๐๐๐๐ก ๐ก๐ โ ๐ด)/๐ป๐ฆ๐๐๐ก๐๐๐ข๐ ๐ = 2/5
๐ด๐ต/๐ด๐ถ=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 = โ(21๐ฅ^2 )
BC = โ21 ๐ฅ
Now,
tan A = (๐๐๐๐ ๐๐๐๐๐ ๐๐ก๐ ๐ก๐ โ ๐ด)/(๐๐๐๐ ๐๐๐๐๐๐๐๐ก ๐ก๐ โ ๐ด)
tan A = ๐ต๐ถ/๐ด๐ต
tan A = (โ21 ๐ฅ)/2๐ฅ
tan A = โ21/2
Thus,
4 + 4 tan2 A
= 4 + 4 (โ21/2)^2
= 4 + 4 ร 21/4
= 4 + 21
= 25

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.