# If x = a cos^3θ and y = a sin^3θ, then find the value of d^2y/dx^2  at θ = π/6. ​

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If x = a cos3θ and y = a sin3θ, then find the value of $\frac{d^2y}{dx^2}$ at θ = $\frac{\pi}{6}.$

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Given,

x = a cos3θ

Differentiating both sides with respect to θ, we get

$\frac{dx}{d\theta}=$ - 3a cos2θ.sin θ  ...(i)

Also,

y = a sin3θ

Differentiating both sides with respect to θ, we get

$\frac{dy}{d\theta}=$  3a sin2θ.cos θ  ...(ii)

Now,