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