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Prove that: sin20^0sin40^0sin60^0sin80^0...

Prove that: `sin20^0sin40^0sin60^0sin80^0=3/(16)`

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Verified by Experts

Given,
`sin20 sin40 sin60 sin80`
`=> sin60[sin20 sin40 sin80]`
`=>(sqrt(3/2))[sin20 sin(60-20) sin(60+20)]`
using formula of
`sinAsin(60-A)sin(60+A)`
`=>(sqrt(3/2))[sin( 3(20)/4)]`
`=>(sqrt(3/2))[sin 60/4]`
...
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sin20^(0)sin40^(0)sin60^(0)sin80^(@)=(3)/(16)

Prove that: sin20^(@)sin40^(0)sin60^(@)sin80^(@)=(3)/(16)

Prove that: i) sin20^(@)sin40^(@)sin60^(@)sin80^(@)=3/16 ii) sin10^(@)sin50^(@)sin60^(@)sin70^(@)=sqrt(3)/16 iii) sin20^(@)sin40^(@)sin80^(@)=sqrt(3)/8

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

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