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prove that sin10 sin50 sin60 sin70 =root 3/ 16

prove that sin20 sin40 sin 60 sin80 =3/16

$1. Given sin10sin50sin60sin70 sin60 (\sin 10 \sin 50 \sin 70) \Rightarrow \frac{\sqrt{3}}{4} (2 \sin 10 \sin 50) \sin 70 \Rightarrow \frac{\sqrt{3}}{4} (\cos 40 - \cos 60) \sin 70 \Rightarrow \frac{\sqrt{3}}{4} \cos 40 \sin 70 - \frac{\sqrt{3}}{4} \times \frac{1}{2} \sin 70 \Rightarrow \frac{\sqrt{3}}{8} (2 \cos 40 \sin 70) - \frac{\sqrt{3}}{8} \sin 70 \Rightarrow \frac{\sqrt{3}}{8} (\sin 110 + \sin 30) - \frac{\sqrt{3}}{8} \sin 70 \Rightarrow \frac{\sqrt{3}}{8} (\sin 110 - \sin 70) + \frac{\sqrt{3}}{8} (\frac{1}{2}) \Rightarrow \frac{\sqrt{3}}{8} (2 \cos 90 \cos 20) + \frac{\sqrt{3}}{16} \Rightarrow \frac{\sqrt{3}}{16} 2. 1. Given sin20sin40sin60sin80 sin60 (\sin 20 \sin 40 \sin 80) \Rightarrow \frac{\sqrt{3}}{4} (2 \sin 20 \sin 40) \sin 80 \Rightarrow \frac{\sqrt{3}}{4} (\cos 20 - \cos 60) \sin 80 \Rightarrow \frac{\sqrt{3}}{4} \cos 20 \sin 80 - \frac{\sqrt{3}}{4} \times \frac{1}{2} \sin 80 \Rightarrow \frac{\sqrt{3}}{8} (2 \cos 20 \sin 80) - \frac{\sqrt{3}}{8} \sin 80 \Rightarrow \frac{\sqrt{3}}{8} (\sin 100 + \sin 60) - \frac{\sqrt{3}}{8} \sin 80 \Rightarrow \frac{\sqrt{3}}{8} (\sin 100 - \sin 80) + \frac{\sqrt{3}}{8} (\frac{\sqrt{2}}{2}) \Rightarrow \frac{\sqrt{3}}{8} (2 \cos 90 \cos 10) + \frac{3}{16} \Rightarrow \frac{3}{16}$

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