Prove that cos pi/5 + cos 2pi/5 + cos 6pi/5 + cos 7pi/5 = 0 Share with your friends Share 10 Varun.Rawat answered this LHS = cosπ5 + cos2π5 + cos6π5 + cos7π5= cos7π5 + cosπ5 + cos6π5 + cos2π5=2 cos 7π5+π52 cos 7π5-π52+ 2 cos 6π5+2π52 cos 6π5-2π52 =2 cos 8π10 . cos 6π10+2 cos 8π10 . cos 4π10=2 cos 4π5 . cos 3π5+2 cos 4π5 . cos 2π5=2 cos 4π5 cos 3π5+ cos 2π5=2 cos 4π5 2 cos 3π5+2π52 cos 3π5-2π52=2 cos 4π52 cos 5π10 cos π10=4 cos 4π5 × cos π10 × cosπ2=4 cos 4π5 × cos π10 × 0 as, cos π2 = 0=0=RHSUsing :cos x + cos y = 2 cos x + y2 . cosx-y2 16 View Full Answer
