sin ^2 frac{pi}{8} + sin ^2 frac{3pi}{8} + si | vedclass

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Question

(B) हम जानते हैं कि $\sin(\pi - 	heta) = \sin 	heta$.$\sin \frac{7\pi}{8} = \sin(\pi - \frac{\pi}{8}) = \sin \frac{\pi}{8}$$\sin \frac{5\pi}{8} = \s

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(B) हम जानते हैं कि $\sin(\pi - 	heta) = \sin 	heta$.$\sin \frac{7\pi}{8} = \sin(\pi - \frac{\pi}{8}) = \sin \frac{\pi}{8}$$\sin \frac{5\pi}{8} = \sin(\pi - \frac{3\pi}{8}) = \sin \frac{3\pi}{8}$इन मानों को व्यंजक में रखने पर:$	ext{व्यंजक} = \sin ^2 \frac{\pi}{8} + \sin ^2 \frac{3\pi}{8} + \sin ^2 \frac{3\pi}{8} + \sin ^2 \frac{\pi}{8}$$= 2(\sin ^2 \frac{\pi}{8} + \sin ^2 \frac{3\pi}{8})$चूंकि $\sin \frac{3\pi}{8} = \sin(\frac{\pi}{2} - \frac{\pi}{8}) = \cos \frac{\pi}{8}$,इसलिए:$= 2(\sin ^2 \frac{\pi}{8} + \cos ^2 \frac{\pi}{8})$सर्वसमिका $\sin ^2 	heta + \cos ^2 	heta = 1$ का उपयोग करने पर:$= 2(1) = 2$

$\sin ^2 \frac{\pi}{8} + \sin ^2 \frac{3\pi}{8} + \sin ^2 \frac{5\pi}{8} + \sin ^2 \frac{7\pi}{8}$ का मान है

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