A) \[\sqrt{mn}\]
B) \[\sqrt{\frac{m}{n}}\]
C) \[4\sqrt{mn}\]
D) None of these
Correct Answer: C
Solution :
| [c] Given, \[\tan \theta +\sin \theta =m\]and \[\tan \theta -\sin \theta =n\] |
| \[{{m}^{2}}-{{n}^{2}}={{(\tan \theta +\sin \theta )}^{2}}-{{(\tan \theta -\sin \theta )}^{2}}\] |
| \[=4\tan \theta \sin \theta =4\sqrt{{{\tan }^{2}}\theta {{\sin }^{2}}\theta }\] |
| \[=4\sqrt{{{\sin }^{2}}\theta \frac{{{\sin }^{2}}\theta }{{{\cos }^{2}}\theta }}=4\sqrt{\frac{{{\sin }^{2}}\theta }{{{\cos }^{2}}\theta }-{{\sin }^{2}}\theta }\] |
| \[=4\sqrt{{{\tan }^{2}}\theta -{{\sin }^{2}}\theta }\] |
| \[=4\sqrt{(\tan \theta +\sin \theta )\,(\tan \theta -\sin \theta )}=4\sqrt{mn}\] |
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