Prove the following identity, where the angles involved are acute angles for which the expressions are defined.
(ix) `(c o s e c\ A\ \ sin\ A)(secA-cosA)=1/(tanA+cotA)`[Hint : Simplify LHS and RHS separately]

Explanation

To prove the identity \((\csc A \sin A)(\sec A - \cos A) = \frac{1}{\tan A + \cot A}\), we will simplify both the left-hand side (LHS) and the right-hand side (RHS) separately.

### Step 1: Simplify the Left-Hand Side (LHS)

The LHS is given as:
\[ (\csc A \sin A)(\sec A - \cos A) \]
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