Value of cos, frac{π }{{10}} ,cos, frac{2π }{{10}} ,cos,frac{4π }{{10}}, cos,frac{8π }

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3.Trigonometrical Ratios, Functions and Identities

normal

The value of $cos\, \frac{\pi }{{10}} \,cos\, \frac{2\pi }{{10}} \,cos\,\frac{4\pi }{{10}}\, cos\,\frac{8\pi }{{10}}\, cos\,\frac{16\pi }{{10}}$ is

$\frac{1 }{{32}}$

$\frac{1}{{16}}$

$\frac{{\cos \,\,\left( {\pi /10} \right)}}{{16}}$

$-\frac{{\sqrt {10\,\, + \,\,2\sqrt 5 } }}{{64}}$

$\pi /10 = \theta$

$E =$$\frac{{2\,\sin \theta \,(\cos \theta \,.\,\cos 2\theta \,.\,\cos 4\theta \,.\cos 8\theta \,.\cos 16\theta \,)}}{{2\,\sin \theta }}$

$=$$\frac{{\sin 32\theta }}{{32\,\sin \theta }}$

$=$$\frac{{\sin (30\theta \, + \,2\theta )}}{{32.\,\sin \theta }}$ $=$ $ – \,\,\frac{1}{{16}}\,\cos \frac{\pi }{{10}}$

$=$ $ – \,\,\frac{1}{{16}}\,\,\sqrt {1 – {{\sin }^2}\pi /10} $

Standard 11

Mathematics

easy

easy

normal

medium

(IIT-1985)

normal