Question

СРОЧНО ПОМОГИТЕ РЕШИТЬ ДАЮ 50 БАЛЛОВ

Answer 1

Формула  "трёх двоечек" :

$\boxed{\ cos^2\alpha =\dfrac{1+cos2\alpha }{2}\ }\\\\\\\dfrac{cos^220^\circ +cos^240^\circ +cos^2100^\circ }{4}=\\\\\\=\dfrac{1}{4}\cdot \Big(\dfrac{1+cos40^\circ }{2}+\dfrac{1+cos80^\circ }{2}+\dfrac{1+cos200^\circ }{2}\Big)=\\\\\\=\dfrac{1}{8}\cdot \Big(3+\underbrace {cos40^\circ +cos80^\circ }+cos(180^\circ +20^\circ )\Big)=\\\\\\=\dfrac{1}{8}\cdot \Big(3+\underbrace {2\cdot cos60^\circ \cdot cos20^\circ }-cos20^\circ \Big)=$

$=\dfrac{1}{8}\cdot \Big(3+2\cdot \dfrac{1}{2}\cdot cos20^\circ -cos20^\circ \Big)=\dfrac{1}{8}\cdot \Big(3+cos20^\circ -cos20^\circ \Big)=\dfrac{3}{8}=0,375$