frac{1 + sin A - cos A}{1 + sin A + cos A} = | vedclass

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Question

(C) Given expression: $\frac{1 + \sin A - \cos A}{1 + \sin A + \cos A}$Using the identities $1 - \cos A = 2 \sin^2 \frac{A}{2}$,$1 + \cos A = 2 \cos^2

Vedclass · Accepted Answer

$	an \frac{A}{2}$

Vedclass · Answer

(C) Given expression: $\frac{1 + \sin A - \cos A}{1 + \sin A + \cos A}$Using the identities $1 - \cos A = 2 \sin^2 \frac{A}{2}$,$1 + \cos A = 2 \cos^2 \frac{A}{2}$,and $\sin A = 2 \sin \frac{A}{2} \cos \frac{A}{2}$:Numerator: $(1 - \cos A) + \sin A = 2 \sin^2 \frac{A}{2} + 2 \sin \frac{A}{2} \cos \frac{A}{2} = 2 \sin \frac{A}{2} (\sin \frac{A}{2} + \cos \frac{A}{2})$Denominator: $(1 + \cos A) + \sin A = 2 \cos^2 \frac{A}{2} + 2 \sin \frac{A}{2} \cos \frac{A}{2} = 2 \cos \frac{A}{2} (\cos \frac{A}{2} + \sin \frac{A}{2})$Dividing the numerator by the denominator:$\frac{2 \sin \frac{A}{2} (\sin \frac{A}{2} + \cos \frac{A}{2})}{2 \cos \frac{A}{2} (\cos \frac{A}{2} + \sin \frac{A}{2})} = \frac{\sin \frac{A}{2}}{\cos \frac{A}{2}} = 	an \frac{A}{2}$Thus,the correct option is $(c)$.

$\frac{1 + \sin A - \cos A}{1 + \sin A + \cos A} = $

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