A) 1/16
B) 1/32
C) 1/8
D) 1/4
Correct Answer: C
Solution :
\[\sin \,{{12}^{o}}\,\sin \,{{48}^{o}}\,\sin \,{{54}^{o}}=\frac{1}{2}\,\left\{ \cos {{36}^{o}}-\cos {{60}^{o}} \right\}\,\cos \,{{36}^{o}}\] \[=\frac{1}{2}\,\left[ \frac{\sqrt{5}+1}{4}-\frac{1}{2} \right]\,\left[ \frac{\sqrt{5}+1}{4} \right]=\frac{1}{2}\,\left[ \frac{\sqrt{5}-1}{4} \right]\,\left[ \frac{\sqrt{5}+1}{4} \right]\] \[=\frac{5-1}{32}=\frac{4}{32}=\frac{1}{8}\].
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