If x = a cos³ θ, y = a sin³ θ, then dy/dx at θ = π/4 is: A. −1 B. 1 C. 0 D. √2 Answer: A) −1 Explanation: dx/dθ = −3a cos² θ sin θ, dy/dθ = 3a sin² θ cos θ. dy/dx = − tan θ. At θ = π/4, tan π/4 = 1, so dy/dx = −1.

imo class 12 continuity and differentiability

If x = a cos³ θ, y = a sin³ θ, then dy/dx at θ = π/4 is:

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If x = a cos³ θ, y = a sin³ θ, then dy/dx at θ = π/4 is:

Answer: A) −1

Explanation: dx/dθ = −3a cos² θ sin θ, dy/dθ = 3a sin² θ cos θ. dy/dx = − tan θ. At θ = π/4, tan π/4 = 1, so dy/dx = −1.