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Prove that cos2 0^(@)cos4 0^(@)cos6 0^(@...

Prove that cos`2 0^(@)cos4 0^(@)cos6 0^(@)cos8 0^(@)=1/16`

Text Solution

Verified by Experts

`cos 20^(@) cos 40^(@)cos 80^(@)cos 60^(@)`
`=cos20^(@) cos (60^(@)-20^(@))cos(60^(@)+20^(@))cos60^(@)`
`=(1)/(4)cos(3xx20^(@))cos60^(@)`
`=(1)/(4)cos^(2)60^(@)=(1)/(4)xx(1)/(4)=(1)/(16)`
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