The equation of the tangent to the curve x = a cos³ θ, y = a sin³ θ at θ = π/4 is:

The equation of the tangent to the curve x = a cos³ θ, y = a sin³ θ at θ = π/4 is:

• A. x + y = a/√2
• B. x − y = a/√2
• C. x + y = a√2
• D. x − y = a√2

Answer: A) x + y = a/√2

Explanation: dx/dθ = −3a cos² θ sin θ, dy/dθ = 3a sin² θ cos θ. dy/dx = −tan θ. At θ = π/4, slope = −1. Point: x = a(1/√2)³ = a/(2√2), y = a/(2√2). Tangent: y − y₁ = −1(x − x₁) → x + y = 2 × a/(2√2) = a/√2.