If `x=a (t+sin t)` and `y=a(1-cos t )` then find `dy/dx`.

Explanation

To find \(\frac{dy}{dx}\) given the parametric equations \(x = a(t + \sin t)\) and \(y = a(1 - \cos t)\), we will follow these steps:

### Step 1: Differentiate \(x\) with respect to \(t\)
We start by differentiating \(x\) with respect to \(t\):
\[ \frac{dx}{dt} = \frac{d}{dt}[a(t + \sin t)] = a\left(\frac{d}{dt}[t] + \frac{d}{dt}[\sin t]\right) = a(1 + \cos t) \]

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