सिद्ध कीजिए कि `cos 20^(@)cos40^(@)cos60^(@)cos 80^(@)=(1)/(16)`

Explanation

बायाँ पक्ष `=cos 20^(@)cos 40^(@) cos 60^(@) cos 80^(@)=(1)/(16)`
`=(1)/(2)cos60^(@)cos 40^(@) (2cos80^(@)cos20^(@))`
`=(1)/(2).(1)/(2)cos40^(@)(2cos80^(@)cos20^(@))`
`=(1)/(4)cos 40^(@)[cos(80^(@)+20^(@))+cos(80^(@)-20^(@))]`
`=(1)/(4)cos 40^(@)(cos 100^(@)+cos 60^(@))`
`=(1)/(4)cos 40^(@)[cos 100^(@)+(1)/(2)]`
`=(1)/(8)(2cos 100^(@)cos 40^(@))+(1)/(8)cos 40^(@)`
`=(1)/(8)[cos (100^(@)+40^(@))+cos(100^(@)-40^(@))]+(1)/(8)cos 40^(@)`
`=(1)/(8)(cos 140^(@)+cos 60^(@))+(1)/(8)cos 40^(@)=(1)/(8)cos 140^(@)+(1)/(16)+(1)/(8)cos 40^(@)`
`=(1)/(8)cos (180^(@)-40^(@))+(1)/(16)+(1)/(8)cos 40^(@)=(-1)/(8)cos 40^(@)+(1)/(16)+(1)/(8)cos 40^(@)`
`=(1)/(16)=` दायाँ पक्ष