Evaluate (sin² 30° + cos² 45°) ÷ (tan² 60° − cot² 45°).

Prove that (1 − cos²θ) cosec²θ = 1.

If tan θ = 4/3, find the value of (sin θ + cos θ)/(sin θ − cos θ).

Prove that tan θ + cot θ = sec θ cosec θ.

Prove that (sec A − tan A)(sec A + tan A) = 1.

If sin θ = 3/5 and θ is acute, find cos θ and tan θ.

If 3 cot θ = 4 and θ is acute, find the value of (5 sin θ − 3 cos θ)/(5 sin θ + 3 cos θ).