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Prove that: sin20^@sin40^@sin80^@=(sqrt(...

Prove that: `sin20^@sin40^@sin80^@=(sqrt(3))/8`

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We have,
L.H.S
sin`20^o`sin`40^o``sin80^0`
On multiplying and divide by 2 and we get `Rightarrow frac{1}{2}[2 sin 20^{circ} sin 40^{circ} sin 80^{circ}]`
`Rightarrow frac{1}{2}[cos (20^{circ}-40^{circ})-cos (20^{circ}+40^{circ})] sin 80^{circ}`
`Rightarrow frac{1}{2}[cos 20^{circ}-cos 60^{circ}] sin 80^{circ}`
`Rightarrow frac{1}{2}[cos 20^{circ}-frac{1}{2}] sin 80^{circ}`
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