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rjawbreakerca 2022-07-03 Answered
Prove that cos 2 π 2 n + 1 + cos 4 π 2 n + 1 + cos 6 π 2 n + 1 + . . . + cos 2 n π 2 n + 1 = 1 2
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Answers (1)

Caiden Barrett
Answered 2022-07-04 Author has 20 answers
k = 1 n cos 2 k π 2 n + 1 = k = 1 n 2 sin π 2 n + 1 cos 2 k π 2 n + 1 2 sin π 2 n + 1 = k = 1 n ( sin ( 2 k + 1 ) π 2 n + 1 sin ( 2 k 1 ) π 2 n + 1 ) 2 sin π 2 n + 1 =
= sin ( 2 n + 1 ) π 2 n + 1 sin π 2 n + 1 2 sin π 2 n + 1 = 1 2

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