Question

The value of (1+cos pi/10) (1+cos 3pi/10) (1+cos 7pi/10) (1+cos 9pi/10)
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Answer 1

Step-by-step explanation:

$= (1 + cos \frac{\pi}{10} )(1 + cos \frac{9\pi}{10} )(1 + cos \frac{3\pi}{10} )(1 + cos \frac{7\pi}{10} ) \\ = (1 + cos \frac{\pi}{10} )(1 + cos(\pi + \frac{\pi}{10} ))(1 + cos \frac{3\pi}{10} )(1 + cos(\pi - \frac{3\pi}{10} )) \\ = (1 + cos \frac{\pi}{10} )(1 - cos \frac{\pi}{10} )(1 + cos \frac{3\pi}{10} )(1 - cos \frac{3\pi}{10} ) \\ = (1 - {cos}^{2} \frac{\pi}{10} )(1 - {cos}^{2} \frac{3\pi}{10} ) \\ = {sin}^{2} \frac{\pi}{10} {sin}^{2} \frac{3\pi}{10} \\ = ( { \frac{ \sqrt{5} - 1 }{4}) }^{2} ( { \frac{ \sqrt{5} + 1}{4}) }^{2} \\ = ( { \frac{ (\sqrt{5} - 1)( \sqrt{5} + 1)}{16} )}^{2} \\ = ( { \frac{4}{16} )}^{2} \\ = \frac{1}{16} \\ \\ hope \: it \: will \: help \: you.$