The value of sin ^2 frac{pi}{8} + sin ^2 frac | vedclass

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(B) We know that $\sin(\pi - 	heta) = \sin 	heta$.$\sin \frac{7\pi}{8} = \sin(\pi - \frac{\pi}{8}) = \sin \frac{\pi}{8}$$\sin \frac{5\pi}{8} = \sin(

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$2$

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(B) We know that $\sin(\pi - 	heta) = \sin 	heta$.$\sin \frac{7\pi}{8} = \sin(\pi - \frac{\pi}{8}) = \sin \frac{\pi}{8}$$\sin \frac{5\pi}{8} = \sin(\pi - \frac{3\pi}{8}) = \sin \frac{3\pi}{8}$Substituting these into the expression:$	ext{Expression} = \sin ^2 \frac{\pi}{8} + \sin ^2 \frac{3\pi}{8} + \sin ^2 \frac{3\pi}{8} + \sin ^2 \frac{\pi}{8}$$= 2(\sin ^2 \frac{\pi}{8} + \sin ^2 \frac{3\pi}{8})$Since $\sin \frac{3\pi}{8} = \sin(\frac{\pi}{2} - \frac{\pi}{8}) = \cos \frac{\pi}{8}$,we have:$= 2(\sin ^2 \frac{\pi}{8} + \cos ^2 \frac{\pi}{8})$Using the identity $\sin ^2 	heta + \cos ^2 	heta = 1$:$= 2(1) = 2$

The value of $\sin ^2 \frac{\pi}{8} + \sin ^2 \frac{3\pi}{8} + \sin ^2 \frac{5\pi}{8} + \sin ^2 \frac{7\pi}{8}$ is

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