Prove that: `sin10^0sin30^0sin50^0sin70^0=1/(16)dot`

Explanation

` L.H.S`

`=sin 10^{circ} sin 30^{circ} sin 50^{circ} sin 70^{circ}`

`=frac{1}{2}(sin 10^{circ} sin 50^{circ} sin 70^{circ})`

`=frac{1}{2}(sin 50^{circ} sin 70^{circ}) sin 10^{circ}`

`=frac{1}{2}[sin (60^{circ}-10^{circ}) sin (60^{circ}+10^{circ})] sin 10^{circ}`

`=frac{1}{2}[(sin ^{2} 60^{circ}-sin ^{2} 10^{circ})] sin 10^{circ}`

`=frac{1}{2}((frac{3}{2})^{2}-sin ^{2} 10^{circ}) sin 10^{circ}`

`=frac{1}{2}[frac{3}{4}-sin ^{2} 10^{circ}] sin 10^{circ}`

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