The value of ^ 3 ((π)/(8)) . cos ((3π)/(8)) + ^ 3 ((π)/(8)) ....

$⇒ \cos^{3}\left(\dfrac{\pi}{8}\right)\cos \left(\dfrac{\pi}{2} - \dfrac{\pi}{8}\right) + \sin^{3}\left(\dfrac{\pi}{8}\right)\sin \left(\dfrac{\pi}{2} - \dfrac{\pi}{8}\right)$

$⇒ \cos^{3}\dfrac{\pi}{8}sin\dfrac{\pi}{8} + \sin^{3}\dfrac{\pi}{8}cos\dfrac{\pi}{8}$

$⇒ sin\dfrac{\pi}{8}cos\dfrac{\pi}{8}\left(\sin^{2}\dfrac{\pi}{8} + \cos^{2}\dfrac{\pi}{8}\right)$

$⇒ \dfrac{1}{2}sin\dfrac{\pi}{4}$

$⇒ \dfrac{1}{2\sqrt{2}}$