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Prove that cos 24^(circ)+cos 55^(circ)+...

Prove that
`cos 24^(circ)+cos 55^(circ)+cos 125^(circ)+cos 204^(circ)+cos 300=(1)/(2)`

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cos 24^(circ)+cos 55^(circ)+cos 125^(circ)+cos 204^(circ)+cos 300^(circ).
.=cos 24^(circ)+cos (90-35)^(circ)+cos (90+35)^(circ)+cos (180+24)^(circ)+cos (270+30)^(circ).
.=cos 24^(circ)+sin 35^(circ)-sin 35^(circ)-cos 24^(circ)+sin 30^(circ)=sin 30^(circ)=(1)/(2).
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