A) \[\frac{1}{2}\]
B) \[\frac{3}{4}\]
C) \[\frac{1}{4}\]
D) None of these
Correct Answer: A
Solution :
| \[f(\theta )=\frac{{{(\cos \theta -\sin \theta )}^{2}}+{{\cos }^{2}}\theta -{{\sin }^{2}}\theta }{2\,\,(\cos \theta -\sin \theta )+(\cos \theta +\sin \theta )}\]\[=\frac{\cos \theta }{\cos \theta +\sin \theta }=\frac{1}{1+\tan \theta }\] |
| \[f\,(11{}^\circ )\,\,f\,(34{}^\circ )=\frac{1}{(1+\tan 11{}^\circ )\,\,(1+\tan 34{}^\circ )}\]\[=\frac{1}{(1+\tan 11{}^\circ )}\,\,\,\frac{1}{1+\tan (45{}^\circ -11{}^\circ )}\] |
| \[=\frac{1}{(1+\tan 11{}^\circ )}\left( \frac{1}{1+\frac{1-\tan 11{}^\circ }{1+\tan 11{}^\circ }} \right)=\frac{1}{2}\] |
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