Question

if tan A = root 3 ,then the value of 2 sec^2A-2 tan^2A .​

Answer 1

Answer:

Value of 2sec²A-2tan²A = 2.

Step-by-step explanation:

Given,

tanA = √3

let,

tanA = √3/1

let,

BC=√3 , AB=1 , AC=?,

According to PHYTHAGAROUS THEROM,

(Hyp)² = (opp.side)² + (adj.side)²

(AC)² = (BC)² + (AB)²

(AC)² = (√3)² + (1)²

(AC)² = 3 + 1

(AC)² = 4

AC = √4

AC = √2×2

:. AC = 2 units

Now consider,

secA = Hyp/adj.side = AC/AB = 2/1

tanA = opp.side/adj.side = BC/AB = √3/1

2sec²A-2tan²A

=> 2(2/1)²-2(√3/1)²

=> 2(4/1)-2(3/1)

=> 2(4) - 2(3)

=> 8 - 6

=> 2

:. 2sec²A-2tan²A = 2.

I hope it helps you!!!