# If x = a (cos t + log tan ), y = a sin t, then find (d^2y/dt^2) and d^2y/dx^2. ​

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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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Given,

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