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Prove the following identity, where the...

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

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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: Simplifying the Left-Hand Side (LHS) The LHS is given as: \[ (\csc A - \sin A)(\sec A - \cos A) \] ...
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