Question

Cosπ/8+ cos3π/8+ cos5π/8+ cos7π/8=0

Answer 1

$LHS = \red { cos \Big(\frac{\pi}{8}\Big) + cos \Big(\frac{3\pi}{8}\Big) + cos \Big(\frac{5\pi}{8}\Big) + cos \Big(\frac{7\pi}{8}\Big)}$

$= cos \Big(\frac{\pi}{8}\Big) + cos \Big(\frac{3\pi}{8}\Big) + cos \Big(\pi - \frac{3\pi}{8}\Big) + cos \Big(\pi - \frac{\pi}{8}\Big)$

$= cos \Big(\frac{\pi}{8}\Big) + cos \Big(\frac{3\pi}{8}\Big) - cos \Big(\frac{3\pi}{8}\Big) - cos \Big(\frac{\pi}{8}\Big)$

/* After cancellation,we get */

$\green {= 0} \\= RHS$

$Hence \: Proved .$

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