If 5 cos θ = 6 sin θ; evaluate : (i) tan θ (ii) 12 sin θ - 3 cos θ/12 sin θ + 3 cos θ

(i) Given: 5 cos θ = 6 sin θ ⇒ ⇒ Hence, tan θ = . (ii) tan θ = ∴ If length of BC = 5x unit, length of AB = 6x unit. In Δ ABC, ⇒ AC2 = BC2 \+ AB2 (∵ AC is hypotenuse) ⇒ AC2 = (5x)2 \+ (6x)2 ⇒ AC2 = 25x2 \+ 36x2 ⇒ AC2 = 61x2 ⇒ AC = ⇒ AC = x sin θ = cos θ = Now, Hence, .