frac{{sin theta }}{{1 - cot theta }} + frac{{ | 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 	h

Vedclass · Accepted Answer

$\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 }}}}$$= \frac{{\sin 	heta }}{{\frac{{\sin 	heta - \cos 	heta }}{{\sin 	heta }}}} + \frac{{\cos 	heta }}{{\frac{{\cos 	heta - \sin 	heta }}{{\cos 	heta }}}}$$= \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 }}$Using the identity $a^2 - b^2 = (a - b)(a + b)$:$= \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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