Prove that the curves x=4 `(costheta+sintheta)` and y=3 `(costheta-sintheta)` represents an ellipse.

Explanation

To prove that the curves \( x = 4(\cos \theta + \sin \theta) \) and \( y = 3(\cos \theta - \sin \theta) \) represent an ellipse, we will eliminate the parameter \( \theta \) and derive a relationship between \( x \) and \( y \).

### Step 1: Rewrite the equations
We start with the given equations:
\[ x = 4(\cos \theta + \sin \theta) \]
\[
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