cos ^2left(frac{7 pi}{8}right)+cos ^2left(fra | vedclass

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(C) हम जानते हैं कि $\cos(\pi - 	heta) = -\cos 	heta$,इसलिए $\cos^2(\pi - 	heta) = \cos^2 	heta$. साथ ही,$\cos(\frac{\pi}{2} - 	heta) = \sin 	he

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(C) हम जानते हैं कि $\cos(\pi - 	heta) = -\cos 	heta$,इसलिए $\cos^2(\pi - 	heta) = \cos^2 	heta$. साथ ही,$\cos(\frac{\pi}{2} - 	heta) = \sin 	heta$,इसलिए $\cos^2(\frac{\pi}{2} - 	heta) = \sin^2 	heta$. दिया गया व्यंजक: $E = \cos^2(\frac{7\pi}{8}) + \cos^2(\frac{5\pi}{8}) + \cos^2(\frac{3\pi}{8}) + \cos^2(\frac{\pi}{8})$. यहाँ $\frac{7\pi}{8} = \pi - \frac{\pi}{8}$,इसलिए $\cos^2(\frac{7\pi}{8}) = \cos^2(\frac{\pi}{8})$. यहाँ $\frac{5\pi}{8} = \pi - \frac{3\pi}{8}$,इसलिए $\cos^2(\frac{5\pi}{8}) = \cos^2(\frac{3\pi}{8})$. अतः,$E = 2\cos^2(\frac{\pi}{8}) + 2\cos^2(\frac{3\pi}{8})$. चूंकि $\frac{3\pi}{8} = \frac{\pi}{2} - \frac{\pi}{8}$,इसलिए $\cos^2(\frac{3\pi}{8}) = \sin^2(\frac{\pi}{8})$. इस मान को $E$ में रखने पर: $E = 2\cos^2(\frac{\pi}{8}) + 2\sin^2(\frac{\pi}{8})$. $E = 2(\cos^2(\frac{\pi}{8}) + \sin^2(\frac{\pi}{8}))$. सर्वसमिका $\sin^2 	heta + \cos^2 	heta = 1$ का उपयोग करने पर,हमें $E = 2(1) = 2$ प्राप्त होता है।

$\cos ^2\left(\frac{7 \pi}{8}\right)+\cos ^2\left(\frac{5 \pi}{8}\right)+\cos ^2\left(\frac{3 \pi}{8}\right)+\cos ^2\left(\frac{\pi}{8}\right)=$

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