If x = a sec³ θ, y = a tan³ θ, then dy/dx at θ = π/4 is:

If x = a sec³ θ, y = a tan³ θ, then dy/dx at θ = π/4 is:

• A. 1/√2
• B. √2
• C. 1
• D. 0

Answer: C) 1

Explanation: dx/dθ = 3a sec² θ sec θ tan θ = 3a sec³ θ tan θ. dy/dθ = 3a tan² θ sec² θ. dy/dx = tan θ / sec θ = sin θ. At θ=π/4, sin π/4 = 1/√2. We check: x = a sec³ θ, y = a tan³ θ. dx/dθ = 3a sec² θ (sec θ tan θ) = 3a sec³ θ tan θ. dy/dθ = 3a tan² θ sec² θ. dy/dx = (3a tan² θ sec² θ)/(3a sec³ θ tan θ) = tan θ / sec θ = sin θ. At π/4, sin π/4 = 1/√2. Option 0 is 1/√2, so correct is 0.