If `x=a(cost+1/2logtan^2t)` and `y=asint` then find `(dy)/(dx)` at `t=pi/4`

Explanation

To find \(\frac{dy}{dx}\) at \(t = \frac{\pi}{4}\) given the equations \(x = a \cos t + \frac{1}{2} \log \tan^2 t\) and \(y = a \sin t\), we will follow these steps:

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

Given:
\[ x = a \cos t + \frac{1}{2} \log \tan^2 t \]
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