If 3 cos A = 4 sin A, find the value of : (i) cos A (ii) 3 - cot2 A + cosec2 A

Given: 3 cos A = 4 sin A ∴ If length of AB = 4x unit, length of BC = 3x unit. In Δ ABC, ⇒ AC2 = AB2 \+ BC2 (∵ AC is hypotenuse) ⇒ AC2 = (4x)2 \+ (3x)2 ⇒ AC2 = 16x2 \+ 9x2 ⇒ AC2 = 25x2 ⇒ AC = ⇒ AC = 5x (i) cos Hence, cos . (ii) 3 - cot2 A + cosec2 A cot cosec Now, 3 - cot2 A + cosec2 A Hence, 3 - cot2 A + cosec2 A = 4.