Ex 8.1, 8
If 3 cot A = 4, check whether ((1 − 𝑡𝑎𝑛2𝐴))/((1 + 𝑡𝑎𝑛2𝐴))= cos2 A – sin2A or not.
3 cot A = 4
cot A = 4/3
So,
tan A = 1/cot𝐴
tan A = 1/((4/3) )
tan A = 3/4
(𝑆𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 ∠𝐴)/(𝑆𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 ∠𝐴) = 3/4
𝐵𝐶/𝐴𝐵 = 3/4
Let BC = 3x
& AB = 4x
We find AC using Pythagoras theorem
(Hypotenuse)2 = (Height)2 + (Base)2
(AC)2 = (AB)2 + (BC)2
(AC)2 = (4x)2 + (ex)2
(AC)2 = 16x2 + 9x2
(AC)2 = 25x2
AC = √(25"x2" )
AC = 5x
sin 𝐴 = (𝑠𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 ∠𝐴)/𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
= 𝐵𝐶/𝐴𝐶
= 3𝑥/5𝑥
= 3/5
Similarly,
cos A = (𝑠𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 𝐴)/𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
= 𝐴𝐵/𝐴𝐶
= 4𝑥/5𝑥
= 4/5
We have to check whether ,
(1 − 𝑡𝑎𝑛2 𝐴)/(1 + 𝑡𝑎𝑛2 𝐴 ) = cos2 A – sin2 A

Made by

Davneet Singh

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.