cos^2 frac{pi}{12} + cos^2 frac{pi}{4} + cos^ | vedclass

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Question

(A) આપેલ પદાવલિ: $\cos^2 \frac{\pi}{12} + \cos^2 \frac{\pi}{4} + \cos^2 \frac{5\pi}{12}$આપણે જાણીએ છીએ કે $\cos^2 	heta = \frac{1 + \cos(2	heta)}{2}

Vedclass · Accepted Answer

$\frac{3}{2}$

Vedclass · Answer

(A) આપેલ પદાવલિ: $\cos^2 \frac{\pi}{12} + \cos^2 \frac{\pi}{4} + \cos^2 \frac{5\pi}{12}$આપણે જાણીએ છીએ કે $\cos^2 	heta = \frac{1 + \cos(2	heta)}{2}$.આ નિત્યસમનો ઉપયોગ કરતા:$= \frac{1 + \cos(\frac{\pi}{6})}{2} + \cos^2(\frac{\pi}{4}) + \frac{1 + \cos(\frac{5\pi}{6})}{2}$$= \frac{1}{2} + \frac{1}{2}\cos(\frac{\pi}{6}) + (\frac{1}{\sqrt{2}})^2 + \frac{1}{2} + \frac{1}{2}\cos(\frac{5\pi}{6})$$= 1 + \frac{1}{2} + \frac{1}{2}(\cos \frac{\pi}{6} + \cos \frac{5\pi}{6})$કારણ કે $\cos(\frac{5\pi}{6}) = -\cos(\frac{\pi}{6})$:$= \frac{3}{2} + \frac{1}{2}(\cos \frac{\pi}{6} - \cos \frac{\pi}{6})$$= \frac{3}{2} + 0 = \frac{3}{2}$.

$\cos^2 \frac{\pi}{12} + \cos^2 \frac{\pi}{4} + \cos^2 \frac{5\pi}{12}$ નું મૂલ્ય શોધો.

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