Question

express thr following as sum or difference of trigonometric:-/7.cos5pie/7​

Answer 1

Answer:

$\frac{ - 1}{ \cos( \frac{5\pi}{7} ) } \\ \\ = \frac{ \cos(\pi) }{ \cos( \frac{5\pi}{7} ) } \\ \\ = \frac{ \cos( \frac{2\pi}{7} + \frac{5\pi}{7} ) }{ \cos( \frac{5\pi}{7} ) } \\ \\ = \frac{ \cos( \frac{5\pi}{7} ) \cos( \frac{2\pi}{7}) - \sin( \frac{5\pi}{7} ) \sin( \frac{2\pi}{7} ) }{\cos( \frac{5\pi}{7} ) } \\ \\ = \cos( \frac{2\pi}{7} ) - \tan( \frac{5\pi}{7} ) \sin( \frac{2\pi}{7} )$