Question

Prove that
${ \cos }^{2} ( \frac{\pi}{10} ) + { \cos }^{2} ( \frac{2\pi}{5} ) + { \cos }^{2} ( \frac{3\pi}{5} ) + { \cos }^{2} ( \frac{9\pi}{10} = 2$
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Answer 1

Step-by-step explanation:

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Answer 2

Answer:-

LHS:-

${ \cos }^{2} ( \frac{\pi}{10} ) + { \cos }^{2} ( \frac{2\pi}{5} ) + { \cos }^{2} ( \frac{3\pi}{5} ) + { \cos }^{2} ( \frac{9\pi}{10} )$

$= { \cos }^{2} ( \frac{\pi}{10}) + { \cos }^{2} ( \frac{\pi}{2} - \frac{\pi}{10} ) + { \cos }^{2} ( \frac{\pi}{2} + \frac{\pi}{10}) + { \cos }^{2} (\pi - \frac{\pi}{10} )$

$= { \cos }^{2}( \frac{\pi}{10} ) + { \sin }^{2} ( \frac{\pi}{10} ) + { \cos }^{2} ( \frac{\pi}{10} ) + { \sin }^{2} ( \frac{\pi}{10} )$

$= 1 + 1$

$= 2$

=R.H.S.

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