If 5 cos A = 3, the value of sec^2 A - tan^2 A is : 1. 1 2. -1 3. 3/4 4. 4/3

Given: 5 cos A = 3 ⇒ cos A = i.e., ∴ If length of AB = 3x unit, length of AC = 5x unit. In Δ ABC, AC2 = BC2 \+ AB2 ⇒ (5x)2 = BC2 \+ (3x)2 ⇒ 25x2 = BC2 \+ 9x2 ⇒ BC2 = 25x2 \- 9x2 ⇒ BC2 = 16x2 ⇒ BC = ⇒ BC = 4x sec A = = tan A = = Now, sec2 A - tan2 A Hence, option 1 is the correct option.