left( frac{sin 2A}{1 + cos 2A} right) left( f | vedclass

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(A) We are given the expression: $\left( \frac{\sin 2A}{1 + \cos 2A} \right) \left( \frac{\cos A}{1 + \cos A} \right)$Using the double angle identitie

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$	an \frac{A}{2}$

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(A) We are given the expression: $\left( \frac{\sin 2A}{1 + \cos 2A} ight) \left( \frac{\cos A}{1 + \cos A} ight)$Using the double angle identities $\sin 2A = 2 \sin A \cos A$ and $1 + \cos 2A = 2 \cos^2 A$,we get:$= \left( \frac{2 \sin A \cos A}{2 \cos^2 A} ight) \left( \frac{\cos A}{1 + \cos A} ight)$$= \left( \frac{\sin A}{\cos A} ight) \left( \frac{\cos A}{1 + \cos A} ight)$$= \frac{\sin A}{1 + \cos A}$Using the half-angle identity $\sin A = 2 \sin \frac{A}{2} \cos \frac{A}{2}$ and $1 + \cos A = 2 \cos^2 \frac{A}{2}$:$= \frac{2 \sin \frac{A}{2} \cos \frac{A}{2}}{2 \cos^2 \frac{A}{2}}$$= \frac{\sin \frac{A}{2}}{\cos \frac{A}{2}} = 	an \frac{A}{2}$.

$\left( \frac{\sin 2A}{1 + \cos 2A} \right) \left( \frac{\cos A}{1 + \cos A} \right) = $

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