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in Continuity and Differentiability by (37.2k points)
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If x = a (cos t + log tan \(\frac{1}{2}\)), y = a sin t, then find \(\frac{d^2y}{dt^2}\) and \(\frac{d^2y}{dx^2}\).

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x = a (cos t + log tan \(\frac{1}{2}\))

Differentiating with respect to t, we get

∵ y =  a sin t

Differentiating with respect to t, we get

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