`(sinalpha + cosalpha)(tanalpha + cotalpha) = secalpha + cosecalpha`

Explanation

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

### Step 1: Write down the left-hand side
\[ LHS = (\sin \alpha + \cos \alpha)(\tan \alpha + \cot \alpha) \]

### Step 2: Substitute the definitions of \(\tan \alpha\) and \(\cot \alpha\)
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