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Prove that sin 10° + sin 20° + sin 40Â...

Prove that sin 10° + sin 20° + sin 40° + sin 50°=sin 70° + sin 80

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`sin 10^(@)+sin20^(@)+sin40^(@)+sin50^(@)`
`=2sin((10^(@)+50^(@))/(2))cos((50^(@)-10^(@))/(2))`
`+2sin((20^(@)+40^(@))/(2))cos((40^(@)-20^(@))/(2))`
`=2sin 30^(@) cos 20^(@)+2sin30^(@)cos10^(@)`
`=2(1)/(2)sin 70^(@)+2(1)/(2)sin80^(@)`
`=sin70^(@)+sin80^(@)`
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