Question

cos 20.cos40.cos80=1/8

Answer 1

$\cos( \alpha ) + \cos(2 \alpha ) + \cos(4 \alpha ) = \\ \cos( \alpha + \cos( {2}^{1} \alpha ) ) + \cos( {2}^{2} \alpha )........ \cos( {2}^{n - 1} ) = \frac{1}{ {2}^{n} }$

therefore using the above formula the answer is

$\frac{1}{ {2}^{n} } = \frac{1}{ {2}^{3} } = \frac{1}{8}$

hence proved,....hope it helps you,...

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