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

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Question

(A) Given expression: $\left( \frac{\sin 2A}{1 + \cos 2A} \right) \left( \frac{\cos A}{1 + \cos A} \right)$Using trigonometric identities:$\sin 2A = 2

Vedclass · Accepted Answer

$	an \frac{A}{2}$

Vedclass · Answer

(A) Given expression: $\left( \frac{\sin 2A}{1 + \cos 2A} ight) \left( \frac{\cos A}{1 + \cos A} ight)$Using trigonometric identities:$\sin 2A = 2 \sin A \cos A$$1 + \cos 2A = 2 \cos^2 A$Substituting these into the first part:$\frac{2 \sin A \cos A}{2 \cos^2 A} = \frac{\sin A}{\cos A} = 	an A$Now,the expression becomes:$	an A \cdot \frac{\cos A}{1 + \cos A} = \frac{\sin A}{\cos A} \cdot \frac{\cos A}{1 + \cos A} = \frac{\sin A}{1 + \cos A}$Using half-angle formulas:$\sin A = 2 \sin \frac{A}{2} \cos \frac{A}{2}$$1 + \cos A = 2 \cos^2 \frac{A}{2}$Therefore:$\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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