frac{sin theta}{1 - cot theta} + frac{cos the | vedclass

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Question

(D) Given expression: $\frac{\sin 	heta}{1 - \cot 	heta} + \frac{\cos 	heta}{1 - 	an 	heta}$Substitute $\cot 	heta = \frac{\cos 	heta}{\sin 	h

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$\cos 	heta + \sin 	heta$

Vedclass · Answer

(D) Given expression: $\frac{\sin 	heta}{1 - \cot 	heta} + \frac{\cos 	heta}{1 - 	an 	heta}$Substitute $\cot 	heta = \frac{\cos 	heta}{\sin 	heta}$ and $	an 	heta = \frac{\sin 	heta}{\cos 	heta}$:$= \frac{\sin 	heta}{1 - \frac{\cos 	heta}{\sin 	heta}} + \frac{\cos 	heta}{1 - \frac{\sin 	heta}{\cos 	heta}}$$= \frac{\sin^2 	heta}{\sin 	heta - \cos 	heta} + \frac{\cos^2 	heta}{\cos 	heta - \sin 	heta}$$= \frac{\sin^2 	heta}{\sin 	heta - \cos 	heta} - \frac{\cos^2 	heta}{\sin 	heta - \cos 	heta}$$= \frac{\sin^2 	heta - \cos^2 	heta}{\sin 	heta - \cos 	heta}$$= \frac{(\sin 	heta - \cos 	heta)(\sin 	heta + \cos 	heta)}{\sin 	heta - \cos 	heta}$$= \sin 	heta + \cos 	heta$

$\frac{\sin \theta}{1 - \cot \theta} + \frac{\cos \theta}{1 - \tan \theta} = $

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