A) \( \Large \frac{1}{16} \) |
B) \( \Large \frac{1}{32} \) |
C) \( \Large \frac{1}{8} \) |
D) \( \Large \frac{1}{4} \) |
C) \( \Large \frac{1}{8} \) |
Now, \( \Large \sin 12 ^{\circ} \sin 48 ^{\circ} \sin 54 ^{\circ} \)
\( \Large = \frac{1}{2} \left(\cos 36 ^{\circ} -\cos 60 ^{\circ} \right) \cos 36 ^{\circ} \)
= \( \Large \frac{1}{2}\left[ \frac{\sqrt{5}+1}{4}-\frac{1}{2} \right]\left[ \frac{\sqrt{5}+1}{4} \right]=\frac{5-1}{32}=\frac{4}{32}=\frac{1}{8} \)