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Question: 2 cos \(\frac{\pi}{13}\)cos \(\frac{9\pi}{13}\) + cos \(\frac{3\pi}{13}\) + cos\(\frac{5\pi}{13}\)...

2 cos π13\frac{\pi}{13}cos 9π13\frac{9\pi}{13} + cos 3π13\frac{3\pi}{13} + cos5π13\frac{5\pi}{13}

A

0

B

1

C

– 1

D

None of these

Answer

0

Explanation

Solution

2 cos π13\frac{\pi}{13}cos 9π13\frac{9\pi}{13} = cos10π13\frac{10\pi}{13} + cos 8π13\frac{8\pi}{13}

= cos(π–3π13)\left( \pi –\frac{3\pi}{13} \right)+ cos (π–5π13)\left( \pi –\frac{5\pi}{13} \right)

̃ = – cos 3π13\frac{3\pi}{13}– cos5π13\frac{5\pi}{13}