Prove that - cos 2-15 cos 4-15 cos 8-15 cos 16-15 - 116

cos2 π15 . cos4 π15 . cos8 π15 . cos16 π15 = sin 2^4 . 2 π1516 . sin2 π15 = sin3 π1516 sin2 π15 = sin(2 π + 2 π15)16 sinπ15 = sin 2π /1516 sin 2π ...

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Trigonometric Ratios of Multiples of an Angle

Prove that : ...

Question

Prove that :
$cos \frac{2 π}{15} cos \frac{4 π}{15} cos \frac{8 π}{15} cos \frac{16 π}{15} = \frac{1}{16}$

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Prove: $cos \frac{2 π}{15} cos \frac{4 π}{15} cos \frac{8 π}{15} cos \frac{16 π}{15} = \frac{1}{16}$

sin x \neq 0

cos x cos 2 x cos 4 x cos 8 x = \frac{sin (2^{4} x)}{2^{4} sin x}

cos \frac{2 π}{15} cos \frac{4 π}{15} cos \frac{8 π}{15} cos \frac{16 π}{15} = \frac{1}{16}

c o s \frac{2 π}{15} c o s \frac{4 π}{15} c o s \frac{8 π}{15} c o s \frac{14 π}{15}

cos \frac{2 π}{15} cos \frac{4 π}{15} cos \frac{8 π}{15} cos \frac{16 π}{15} = \frac{1}{16}

A

{sin}^{4} A - 2 {sin}^{2} A - 1

2 π

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