A) \[\frac{1}{2}\]
B) \[\frac{2-\sqrt{3}}{2}\]
C) \[\frac{1}{4}\]
D) \[\frac{3}{4}\]
Correct Answer: D
Solution :
| [d] \[\tan \frac{\pi }{8}\cdot \tan \frac{\pi }{12}\cdot tan\frac{3\pi }{8}.\] \[\tan \frac{5\pi }{12}-{{\sin }^{2}}\frac{\pi }{6}\] \[=\tan \frac{\pi }{8}\cdot \tan \frac{\pi }{12}\cdot \cot \left( \frac{\pi }{2}-\frac{3\pi }{8} \right).\cot \left( \frac{\pi }{2}-\frac{5\pi }{12} \right)-\frac{1}{4}\] \[=\tan \frac{\pi }{8}\cdot tan\frac{\pi }{12}\cot \frac{\pi }{8}\cot \frac{\pi }{12}-\frac{1}{4}\] \[=1-\frac{1}{4}=\frac{3}{4}\] |
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