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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

Verified by Experts

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

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

Knowledge Check

  • sin20^(@)sin40^(@)sin60^(@)sin80^(@)=?

    A
    `1/16`
    B
    `3/16`
    C
    `-3/16`
    D
    None of these

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