Prove that : `sintheta(1+tantheta)+costheta(1+cottheta)=cosectheta+sectheta`

Explanation

To prove the identity \( \sin \theta (1 + \tan \theta) + \cos \theta (1 + \cot \theta) = \csc \theta + \sec \theta \), we will start with the left-hand side (LHS) and simplify it step by step until we reach the right-hand side (RHS).

### Step 1: Write down the LHS
\[ \text{LHS} = \sin \theta (1 + \tan \theta) + \cos \theta (1 + \cot \theta) \]

### Step 2: Expand the terms
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