If `x=a(cost+logtan(t/2))` , `y=asint` , evaluate `(d^2y)/(dx^2)` at `t=pi/3` .

Explanation

To solve the problem of finding \(\frac{d^2y}{dx^2}\) at \(t = \frac{\pi}{3}\) given the equations \(x = a(\cos t + \log \tan(\frac{t}{2}))\) and \(y = a \sin t\), we will follow these steps:

### Step 1: Differentiate \(y\) with respect to \(t\)

Given:
\[ y = a \sin t \]
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