Question

10 корень из 2 *2cos^2 15п/8 -5корень2

Answer 1

Воспользуемся формулой понижения степеней $\cos^2 \alpha = \frac{1+\cos2 \alpha }{2}$

$10 \sqrt{2} \cdot 2\cos^2 \frac{15 \pi }{8} -5\sqrt{2} =10\sqrt{2} \cdot2\cdot \dfrac{1+\cos \frac{15 \pi }{4} }{2} -5\sqrt{2} =\\ \\ \\ =10\sqrt{2} (1+\cos(4 \pi - \frac{\pi}{4} ))-5\sqrt{2} =10\sqrt{2} (1+\cos \frac{\pi}{4})-5\sqrt{2} =\\ \\ \\ =10\sqrt{2} (1+ \frac{1}{ \sqrt{2} } )-5\sqrt{2} =10\sqrt{2} +10-5\sqrt{2} =10+5\sqrt{2}$