A) \[8\]
B) \[4\sqrt{3}\]
C) \[8\sqrt{3}\]
D) \[16\sqrt{3}\]
Correct Answer: C
Solution :
| [c] We have, \[8\sqrt{3}\cos e{{c}^{2}}30{}^\circ \,\sin 60{}^\circ \cos 60{}^\circ \] |
| \[{{\cos }^{2}}45{}^\circ \sin 45{}^\circ \tan 30{}^\circ \cos e{{c}^{3}}45{}^\circ \] |
| \[=8\sqrt{3}\cdot \frac{1}{{{\sin }^{2}}30{}^\circ }\cdot \sin 60{}^\circ \cdot \cos 60{}^\circ \cdot {{\cos }^{2}}45{}^\circ \] |
| \[\cdot \sin 45{}^\circ \cdot \frac{\sin 30{}^\circ }{\cos 30{}^\circ }\cdot \frac{1}{{{\sin }^{3}}45{}^\circ }\] |
| \[=8\sqrt{3}\cdot \frac{1}{{{\sin }^{2}}30{}^\circ }\cdot \sin 60{}^\circ \cdot \cos 60{}^\circ \cdot {{\cos }^{2}}45{}^\circ \cdot \frac{1}{\cos 30{}^\circ }\cdot \frac{1}{{{\sin }^{2}}45{}^\circ }\] |
| \[=8\sqrt{3}\cdot \frac{1}{1/2}\cdot \frac{\sqrt{3}}{2}\cdot \frac{1}{2}\cdot {{\left( \frac{1}{\sqrt{2}} \right)}^{2}}\cdot \frac{1}{\sqrt{3}/2}\cdot \frac{1}{{{(1/\sqrt{2})}^{2}}}\] |
| \[=8\sqrt{3}\cdot 2\cdot \frac{\sqrt{3}}{2}\cdot \frac{1}{2}\cdot \frac{1}{2}\cdot \frac{2}{\sqrt{3}}\cdot 2=8\sqrt{3}\] |
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