Trigonometric Identities Question 148
Question: $ \frac{\sin \theta }{1-\cot \theta }+\frac{\cos \theta }{1-\tan \theta }= $
[Karnataka CET 1998]
Options:
A) 0
B) 1
C) $ \cos \theta -\sin \theta $
D) $ \cos \theta +\sin \theta $
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Answer:
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 $ .
BETA
