Задача 26619 [m] \sqrt{8} - \sqrt{32} \sin^{2}...

u92255227193

22.04.2018

[m] \sqrt{8} - \sqrt{32} \sin^{2} \frac{11\pi}{8} [/m]

SOVA

22.04.2018

sqrt(32)=2sqrt(8)

sqrt(8)-sqrt(32)sin^2(11Pi/8)=sqrt(8)*(1-2sin^2(11Pi/8))=
=sqrt(8)*cos2*(11Pi/8)=sqrt(8)*cos(11Pi/4)=
=sqrt(8)* cos((12Pi-Pi)/4)=sqrt(8)*cos(3Pi-(Pi/4))=
=sqrt(8)*(-cos(Pi/4))=sqrt(8)*(-sqrt(2)/2)=-4sqrt(2)