cos ^3left(frac{pi}{8}right) cos left(frac{3 | vedclass

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(A) ધારો કે આપેલ પદાવલિ $E = \cos ^3\left(\frac{\pi}{8}\right) \cos \left(\frac{3 \pi}{8}\right)+\sin ^3\left(\frac{\pi}{8}\right) \sin \left(\frac{3

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$\frac{1}{2 \sqrt{2}}$

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(A) ધારો કે આપેલ પદાવલિ $E = \cos ^3\left(\frac{\pi}{8}\right) \cos \left(\frac{3 \pi}{8}\right)+\sin ^3\left(\frac{\pi}{8}\right) \sin \left(\frac{3 \pi}{8}\right)$ છે.નિત્યસમ $\cos \left(\frac{3 \pi}{8}\right) = \sin \left(\frac{\pi}{8}\right)$ અને $\sin \left(\frac{3 \pi}{8}\right) = \cos \left(\frac{\pi}{8}\right)$ નો ઉપયોગ કરતા:$E = \cos ^3\left(\frac{\pi}{8}\right) \sin \left(\frac{\pi}{8}\right) + \sin ^3\left(\frac{\pi}{8}\right) \cos \left(\frac{\pi}{8}\right)$$\sin \left(\frac{\pi}{8}\right) \cos \left(\frac{\pi}{8}\right)$ સામાન્ય લેતા:$E = \sin \left(\frac{\pi}{8}\right) \cos \left(\frac{\pi}{8}\right) \left[ \cos ^2\left(\frac{\pi}{8}\right) + \sin ^2\left(\frac{\pi}{8}\right) \right]$પાયથાગોરિયન નિત્યસમ $\sin ^2 A + \cos ^2 A = 1$ નો ઉપયોગ કરતા:$E = \sin \left(\frac{\pi}{8}\right) \cos \left(\frac{\pi}{8}\right) \cdot (1) = \sin \left(\frac{\pi}{8}\right) \cos \left(\frac{\pi}{8}\right)$બમણા ખૂણાના સૂત્ર $\sin (2A) = 2 \sin A \cos A$ નો ઉપયોગ કરતા:$E = \frac{1}{2} \sin \left(\frac{\pi}{4}\right) = \frac{1}{2} \cdot \frac{1}{\sqrt{2}} = \frac{1}{2 \sqrt{2}}$.

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

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