Prove that
` ( "cosec" A - sin A)(sec A- cos A)=(1)/((tan A+ cot A)). `

Explanation

To prove the identity \( ( \csc A - \sin A)(\sec A - \cos A) = \frac{1}{\tan A + \cot A} \), we will start by simplifying the left-hand side (LHS) and then show that it equals the right-hand side (RHS).

### Step 1: Start with the left-hand side
\[ LHS = (\csc A - \sin A)(\sec A - \cos A) \]

### Step 2: Substitute the identities for cosecant and secant
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