If x and y are connected parametrically by the equations given, without eliminating the parameter, Find `(dy)/(dx)`.
`x=a(cost+logtan((t)/(2))), y=asint`

Explanation

To find \(\frac{dy}{dx}\) for the parametric equations given by \(x = a \cos t + \log \tan \left(\frac{t}{2}\right)\) and \(y = a \sin t\), we will follow these steps:

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

We start by differentiating \(x\):
\[ \frac{dx}{dt} = \frac{d}{dt} \left( a \cos t + \log \tan \left(\frac{t}{2}\right) \right) \]
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