frac{sin theta}{1-cot theta} + frac{cos theta | 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 	heta

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}$: $= \frac{\sin 	heta}{1-\frac{\cos 	heta}{\sin 	heta}} + \frac{\cos 	heta}{1-\frac{\sin 	heta}{\cos 	heta}}$ $= \frac{\sin^2 	heta}{\sin 	heta - \cos 	heta} + \frac{\cos^2 	heta}{\cos 	heta - \sin 	heta}$ $= \frac{\sin^2 	heta}{\sin 	heta - \cos 	heta} - \frac{\cos^2 	heta}{\sin 	heta - \cos 	heta}$ $= \frac{\sin^2 	heta - \cos^2 	heta}{\sin 	heta - \cos 	heta}$ 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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