Show that the normal at any point `theta`to the curve`x=acostheta+athetasintheta,``y=asintheta-athetacostheta`is at a constant distance from the origin.

Explanation

To show that the normal at any point \(\theta\) to the curve defined by the parametric equations \(x = a \cos \theta + a \theta \sin \theta\) and \(y = a \sin \theta - a \theta \cos \theta\) is at a constant distance from the origin, we will follow these steps:

### Step 1: Find the derivatives \(dx/d\theta\) and \(dy/d\theta\)

Given:
\[ x = a \cos \theta + a \theta \sin \theta \]
...