Question

10 корней из 2 × cos^2(15п/8)-5 корней из 2

Answer 1

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

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

Answer 2

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