A) 1/16
B) 1/32
C) 1/8
D) 1/4
Correct Answer: C
Solution :
\[\sin {{12}^{o}}\sin {{48}^{o}}\sin {{54}^{o}}\] \[=\frac{1}{2}[2\sin {{12}^{o}}\sin {{48}^{o}}]\sin ({{90}^{o}}-{{36}^{o}})\] \[=\frac{1}{2}[\cos {{36}^{o}}-\cos {{60}^{o}}]\cos {{36}^{o}}\] \[=\frac{1}{2}\left[ \frac{\sqrt{5}+1}{4}-\frac{1}{2} \right]\left( \frac{\sqrt{5}+1}{4} \right)\] \[=\frac{1}{32}[5+1+2\sqrt{5}-2(\sqrt{5}+1)]\] \[=\frac{1}{32}[4]=\frac{1}{8}\]
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