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Prove that sin 20^(@) sin 40^(@) sin 60^...

Prove that `sin 20^(@) sin 40^(@) sin 60^(@) sin 80^(@)=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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Knowledge Check

  • cos 60^(@) sin 30^(@) +cos 30^(@) sin 60^(@)=

    A
    `90^(@)`
    B
    `(1)/(2)`
    C
    `(sqrt(3))/(2)`
    D
    `1`

  • co60^(@)sin30^(@)+cos30^(@)sin60^(@) =___.

    A
    `1`
    B
    `(1)/(sqrt(2))`
    C
    `(1)/(2)`
    D
    `(sqrt(3))/(2)`

  • cos30^(@)sin60^(@)+cos60^(@)sin30^(@)= ……………………

    A
    1
    B
    0
    C
    -1
    D
    `sqrt(3)/(2)`

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