Evaluate cos &#x2061;<!-- ⁡ --> &#x03C0;<!-- π --> 7 </mfrac> cos &#x2

vittorecostao1

vittorecostao1

Answered question

2022-06-23

Evaluate cos π 7 cos 2 π 7 cos 4 π 7

Answer & Explanation

Cahokiavv

Cahokiavv

Beginner2022-06-24Added 31 answers

Multiply by 8 sin π 7 and simplify using 2 sin x cos x = sin 2 x three times:
8 sin π 7 cos π 7 cos 2 π 7 cos 4 π 7 = 4 sin 2 π 7 cos 2 π 7 cos 4 π 7 = 2 sin 4 π 7 cos 4 π 7 = sin 8 π 7
But you also have:
sin 8 π 7 = sin ( π 8 π 7 ) = sin π 7
Now divide again by 8 sin π 7

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