Given : 4 cot A = 3, find : (i) sin A (ii) sec A (iii) cosec^2 A - cot^2 A

Given: 4 cot A = 3 cot i.e., ∴ If length of AB = 3x unit, length of BC = 4x unit. In Δ ABC, ⇒ AC2 = AB2 \+ BC2 (∵ AC is hypotenuse) ⇒ AC2 = (3x)2 + (4x)2 ⇒ AC2 = 9x2 + 16x2 ⇒ AC2 = 25x2 ⇒ AC = ⇒ AC = 5x (i) sin Hence, sin . (ii) sec Hence, sec . (iii) cosec2 A - cot2 A cosec cot Now, Hence, cosec2 A - cot2 A = 1.