A) \[\frac{2}{3}\]
B) \[\frac{1}{2}\]
C) \[\frac{1}{8}\]
D) \[\frac{1}{3}\]
E) 3
Correct Answer: C
Solution :
\[sin\text{ }12{}^\circ \text{ }sin\text{ }48{}^\circ \text{ }sin\text{ }54{}^\circ \] \[=\frac{1}{2}[\cos 36{}^\circ -\cos 60{}^\circ ]\sin 54{}^\circ \] \[=\frac{1}{2}\left[ \frac{\sqrt{5}+1}{4}-\frac{1}{2} \right]\left[ \frac{\sqrt{5}+1}{4} \right]\] \[=\frac{1}{2}\left[ \frac{\sqrt{5}-1}{4} \right]\left[ \frac{\sqrt{5}+1}{4} \right]=\frac{5-1}{2\times 4\times 4}\] \[=\frac{1}{8}\]
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