Find the value of sin &#x2061;<!-- ⁡ --> &#x03C0;<!-- π --> 7 </mfrac> sin &#

Taniyah Estrada

Taniyah Estrada

Answered question

2022-06-16

Find the value of
sin π 7 sin 2 π 7 sin 3 π 7 sin π 14 sin 3 π 14 sin 5 π 14

Answer & Explanation

Eli Shaffer

Eli Shaffer

Beginner2022-06-17Added 16 answers

It can be seen as an instance of the well-known identity:
(1) k = 1 n 1 sin ( k π n ) = 2 n 2 n
that for n = 14 gives:
(2) [ k = 1 6 sin ( k π 14 ) ] 2 = 14 2 13
from which:
(3) k = 1 6 sin ( k π 14 ) = 7 64 .

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