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Prove that: "sin"20^0"sin"40^0"sin"60^0"...

Prove that: `"sin"20^0"sin"40^0"sin"60^0"sin"80^0=3/(16)`

Text Solution

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`sin20^(@)sin40^(@)sin60^(@)sin80^(@)`
`=sin60^(@)sin20^(@)sin(60^(@)-20^(@))sin(60^(@)+20^(@))`
`=(1)/(4)sin60^(@)sin(3xx20^(@))=(1)/(4)sin^(2)60^(@)=(3)/(16)`
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