A) 0
B) 1
C) \[\cos \theta -\sin \theta \]
D) \[\cos \theta +\sin \theta \]
Correct Answer: D
Solution :
\[\frac{\sin \theta }{1-\cot \theta }+\frac{\cos \theta }{1-\tan \theta }\]\[=\frac{\sin \theta \,.\,\sin \theta }{\,\sin \theta -\cos \theta }+\frac{\cos \theta \,.\cos \theta }{\cos \theta -\sin \theta }\] \[=\frac{({{\cos }^{2}}\theta -{{\sin }^{2}}\theta )}{(\cos \theta -\sin \theta )}=\cos \theta +\sin \theta \].
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