2 sin(frac{pi}{8}) sin(frac{2pi}{8}) sin(frac | vedclass

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(C) माना व्यंजक $E = 2 \sin(\frac{\pi}{8}) \sin(\frac{2\pi}{8}) \sin(\frac{3\pi}{8}) \sin(\frac{5\pi}{8}) \sin(\frac{6\pi}{8}) \sin(\frac{7\pi}{8})$ ह

Vedclass · Accepted Answer

$\frac{1}{8}$

Vedclass · Answer

(C) माना व्यंजक $E = 2 \sin(\frac{\pi}{8}) \sin(\frac{2\pi}{8}) \sin(\frac{3\pi}{8}) \sin(\frac{5\pi}{8}) \sin(\frac{6\pi}{8}) \sin(\frac{7\pi}{8})$ है।गुणधर्म $\sin(\pi - 	heta) = \sin 	heta$ का उपयोग करते हुए,$\sin(\frac{7\pi}{8}) = \sin(\frac{\pi}{8})$,$\sin(\frac{6\pi}{8}) = \sin(\frac{2\pi}{8})$,और $\sin(\frac{5\pi}{8}) = \sin(\frac{3\pi}{8})$ है।इन मानों को प्रतिस्थापित करने पर,$E = 2 \sin^2(\frac{\pi}{8}) \sin^2(\frac{2\pi}{8}) \sin^2(\frac{3\pi}{8})$.चूंकि $\sin(\frac{2\pi}{8}) = \sin(\frac{\pi}{4}) = \frac{1}{\sqrt{2}}$,इसलिए $\sin^2(\frac{2\pi}{8}) = \frac{1}{2}$ है।अतः,$E = 2 \cdot \frac{1}{2} \cdot \sin^2(\frac{\pi}{8}) \sin^2(\frac{3\pi}{8}) = \sin^2(\frac{\pi}{8}) \cos^2(\frac{\pi}{8})$ (क्योंकि $\sin(\frac{3\pi}{8}) = \cos(\frac{\pi}{8})$)।$E = (\sin(\frac{\pi}{8}) \cos(\frac{\pi}{8}))^2 = (\frac{1}{2} \sin(\frac{2\pi}{8}))^2 = (\frac{1}{2} \sin(\frac{\pi}{4}))^2 = (\frac{1}{2} \cdot \frac{1}{\sqrt{2}})^2 = \frac{1}{4 \cdot 2} = \frac{1}{8}$।

$2 \sin(\frac{\pi}{8}) \sin(\frac{2\pi}{8}) \sin(\frac{3\pi}{8}) \sin(\frac{5\pi}{8}) \sin(\frac{6\pi}{8}) \sin(\frac{7\pi}{8})$ का मान है:

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