A) \[\sqrt{3}\,\cos \theta \]
B) \[3\,\cos \theta \]
C) \[3\,\sin \theta \]
D) \[\sqrt{3}\,\sin \theta \]
Correct Answer: D
Solution :
| [d]\[\frac{3{{\cos }^{2}}\theta +2\cos \theta }{3\cos \theta +2}\] |
| \[=\frac{3\times {{(\sqrt{3}\sin \theta )}^{2}}+2\times \sqrt{3}\sin \theta }{3\times \sqrt{3}\sin \theta +2}\]\[(\cos \theta =\sqrt{3}\sin \theta )\] |
| \[=\frac{3\times 3{{\sin }^{2}}\theta +2\sqrt{3}\sin \theta }{3\sqrt{3}\sin \theta +2}=\frac{\sqrt{3}\sin \theta (3\sqrt{3}\sin \theta +2)}{(3\sqrt{3}\sin \theta +2)}\] |
| \[=\sqrt{3}\sin \theta \] |
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