আমাদের টেলিগ্রাম চ্যানেলে যুক্ত হোন

Prove that, cos $\frac{3\pi }{13}$ + cos $\frac{5\pi }{13}$- 2 cos $\frac{9\pi }{13}$ cos $\frac{12\pi }{13}$=0

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Prove that, cos $\frac{3\pi }{13}$ + cos $\frac{5\pi }{13}$- 2 cos $\frac{9\pi }{13}$ cos $\frac{12\pi }{13}$=0

Solution:

L.H.S= cos $\frac{3\pi }{13}$+ cos $\frac{5\pi }{13}$   – 2 cos $\frac{9\pi }{13}$   cos $\frac{12\pi }{13}$
= 2 cos $\frac{\frac{3\pi }{13} + \frac{5\pi }{13}}{2}$ cos$\frac{\frac{3\pi }{13} – \frac{5\pi }{13}}{2}$ – 2 cos $\frac{9\pi }{13}$cos $\frac{12\pi }{13}$
= 2 cos $\frac{4\pi }{13}$ cos $\left( – \frac{\pi }{13}\right)$ – 2 cos $\frac{9\pi }{13}$ cos $\frac{12\pi }{13}$
= 2 cos $\frac{4\pi }{13}$   cos $\frac{\pi }{13}$ – 2 cos $\left(\pi  – \frac{4\pi }{13}\right)$ cos $\left(\pi  – \frac{\pi }{13}\right)$
= 2 cos $\frac{4\pi }{13}$ cos $\frac{\pi }{13}$   – 2 cos $\frac{4\pi }{13}$ cos $\frac{\pi }{13}$  
= 0 =R.H.S [Proved]

আরও দেখুন

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  3. Prove that,$\sin \left(\frac{2\pi }{3} + \theta \right) – sin\left(\frac{2\pi }{3} – \theta \right) + sin\theta$ = 0
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