For the next two (02) items that follow: cosecθ - sinθ = p³ and secθ - cosθ = q³ What is p⁴q² + p²q⁴ equal to?

p³ = cos²θ/sinθ, so p² = (cos²θ/sinθ)^(2/3). Similarly q² = (sin²θ/cosθ)^(2/3). Then p²q² = (cos²θ · sin²θ/(sinθ · cosθ))^(2/3) = (sinθ · cosθ)^(2/3). And p⁴q² + p²q⁴ = p²q²(p² + q²). Note p² + q² = (cos²θ/sinθ)^(2/3) + (sin²θ/cosθ)^(2/3) = cos^(4/3)θ/sin^(2/3)θ + sin^(4/3)θ/cos^(2/3)θ = (cos²θ + sin²θ)/(sin^(2/3)θ · cos^(2/3)θ) = 1/(sinθ cosθ)^(2/3). So p⁴q² + p²q⁴ = (sinθ cosθ)^(2/3) · 1/(sinθ cosθ)^(2/3) = 1.