For the next two (02) items that follow: cosecθ - sinθ = p³ and secθ - cosθ = q³ What is tanθ equal to?

cosecθ - sinθ = 1/sinθ - sinθ = (1 - sin²θ)/sinθ = cos²θ/sinθ = p³. Similarly, secθ - cosθ = (1 - cos²θ)/cosθ = sin²θ/cosθ = q³. Dividing: p³/q³ = (cos²θ/sinθ)/(sin²θ/cosθ) = cos³θ/sin³θ = cot³θ. So p/q = cotθ, hence tanθ = q/p. Wait — that gives tanθ = q/p, option (b). Let me recheck the division: (cos²θ/sinθ) × (cosθ/sin²θ) = cos³θ/sin³θ = cot³θ. So p³/q³ = cot³θ, p/q = cotθ, tanθ = q/p. The answer is q/p, option (b).