cos ^4 frac{pi}{8}+cos ^4 frac{3 pi}{8}+cos ^ | vedclass

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Question

(B) આપણે જાણીએ છીએ કે $\cos(\pi - 	heta) = -\cos 	heta$,તેથી $\cos^4(\pi - 	heta) = \cos^4 	heta$. આમ,$\cos^4 \frac{7\pi}{8} = \cos^4 \frac{\pi}{8

Vedclass · Accepted Answer

$\frac{3}{2}$

Vedclass · Answer

(B) આપણે જાણીએ છીએ કે $\cos(\pi - 	heta) = -\cos 	heta$,તેથી $\cos^4(\pi - 	heta) = \cos^4 	heta$. આમ,$\cos^4 \frac{7\pi}{8} = \cos^4 \frac{\pi}{8}$ અને $\cos^4 \frac{5\pi}{8} = \cos^4 \frac{3\pi}{8}$. પદાવલિ $2(\cos^4 \frac{\pi}{8} + \cos^4 \frac{3\pi}{8})$ બને છે. $\cos^2 	heta = \frac{1 + \cos 2	heta}{2}$ નો ઉપયોગ કરતા,$\cos^4 	heta = \frac{3 + 4\cos 2	heta + \cos 4	heta}{8}$. $	heta = \frac{\pi}{8}$ માટે,$\cos^4 \frac{\pi}{8} = \frac{3 + 2\sqrt{2}}{8}$. $	heta = \frac{3\pi}{8}$ માટે,$\cos^4 \frac{3\pi}{8} = \frac{3 - 2\sqrt{2}}{8}$. સરવાળો કરતા,$2(\frac{3 + 2\sqrt{2}}{8} + \frac{3 - 2\sqrt{2}}{8}) = 2(\frac{6}{8}) = \frac{3}{2}$.

$\cos ^4 \frac{\pi}{8}+\cos ^4 \frac{3 \pi}{8}+\cos ^4 \frac{5 \pi}{8}+\cos ^4 \frac{7 \pi}{8}=$

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