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

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Question

(D) We have $\frac{\cos A}{1 - \sin A}$.Multiply the numerator and denominator by $(1 + \sin A)$:$\frac{\cos A(1 + \sin A)}{(1 - \sin A)(1 + \sin A)}

Vedclass · Accepted Answer

$	an \left( \frac{\pi}{4} + \frac{A}{2} ight)$

Vedclass · Answer

(D) We have $\frac{\cos A}{1 - \sin A}$.Multiply the numerator and denominator by $(1 + \sin A)$:$\frac{\cos A(1 + \sin A)}{(1 - \sin A)(1 + \sin A)} = \frac{\cos A(1 + \sin A)}{1 - \sin^2 A} = \frac{\cos A(1 + \sin A)}{\cos^2 A} = \frac{1 + \sin A}{\cos A}$.Using half-angle identities $\sin A = 2 \sin \frac{A}{2} \cos \frac{A}{2}$ and $\cos A = \cos^2 \frac{A}{2} - \sin^2 \frac{A}{2}$:$= \frac{(\cos \frac{A}{2} + \sin \frac{A}{2})^2}{(\cos \frac{A}{2} - \sin \frac{A}{2})(\cos \frac{A}{2} + \sin \frac{A}{2})} = \frac{\cos \frac{A}{2} + \sin \frac{A}{2}}{\cos \frac{A}{2} - \sin \frac{A}{2}}$.Dividing numerator and denominator by $\cos \frac{A}{2}$:$= \frac{1 + 	an \frac{A}{2}}{1 - 	an \frac{A}{2}} = 	an \left( \frac{\pi}{4} + \frac{A}{2} ight)$.

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

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