Question

The expression $\cos(\frac{1}{15}\pi)\cos(\frac{2}{15}\pi)\cos(\frac{4}{15}\pi)\cos(\frac{8}{15}\pi)$ equals (A) $\frac{\sqrt{5}-1}{2}$ (B) $\frac{1}{16}$ (C) $\frac{1-\sqrt{5}}{2}$ (D) $-\frac{1}{16}$ (E) $-\frac{1}{15}$

Name: the expression cosfrac115picosfrac215picosfrac415picosfrac815pi equals a fracsqrt5 12 b frac116 c frac1 sqrt52 d frac116 e frac115 50732
Uploaded: 2021-07-20T13:11:49-08:00
Duration: 2 min 36 s
Channel: Viraj Gaggar
Description: the expression cosfrac115picosfrac215picosfrac415picosfrac815pi equals a fracsqrt5 12 b frac116 c frac1 sqrt52 d frac116 e frac115 50732

          The expression $\cos(\frac{1}{15}\pi)\cos(\frac{2}{15}\pi)\cos(\frac{4}{15}\pi)\cos(\frac{8}{15}\pi)$ equals
(A) $\frac{\sqrt{5}-1}{2}$
(B) $\frac{1}{16}$
(C) $\frac{1-\sqrt{5}}{2}$
(D) $-\frac{1}{16}$
(E) $-\frac{1}{15}$

$the expression cosfrac115picosfrac215picosfrac415picosfrac815pi equals a fracsqrt5 12 b frac116 c frac1 sqrt52 d frac116 e frac115 50732$

Added by Ivan S.

Introductory and Intermediate Algebra for College Students 4th

Robert Blitzer 4th Edition

Instant Answer

Solved by Expert Viraj Gaggar

07/20/2021

Step 1

$P = \cos(\frac{1}{15}\pi)\cos(\frac{2}{15}\pi)\cos(\frac{4}{15}\pi)\cos(\frac{8}{15}\pi)$ We use the product-to-sum formula for cosine, or more specifically, the identity: $\sin(2x) = 2\sin(x)\cos(x)$, which can be rearranged as $\cos(x) = Show more…

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The expression $\cos(\frac{1}{15}\pi)\cos(\frac{2}{15}\pi)\cos(\frac{4}{15}\pi)\cos(\frac{8}{15}\pi)$ equals (A) $\frac{\sqrt{5}-1}{2}$ (B) $\frac{1}{16}$ (C) $\frac{1-\sqrt{5}}{2}$ (D) $-\frac{1}{16}$ (E) $-\frac{1}{15}$