Question

Помогите, пожалуйста, с решением

Answer 1

$Cos^{2}alpha-Cos(alpha+frac{pi }{6})Cos(alpha-frac{pi }{6})=Cos^{2}alpha-frac{1}{2}(Cos(alpha+frac{pi }{6}+alpha-frac{pi }{6})+Cos(alpha+frac{pi }{6}-alpha+frac{pi }{6}))=Cos^{2}alpha-frac{1}{2}(Cos2alpha+Cosfrac{pi }{3})=Cos^{2}alpha-frac{1}{2}Cos2alpha-frac{1}{2}*Cosfrac{pi }{3}=Cos^{2}alpha-frac{1}{2}(2Cos^{2}alpha} -1)-frac{1}{2}*frac{1}{2}=Cos^{2}alpha -Cos^{2} alpha+frac{1}{2}-frac{1}{4}=frac{1}{4}=0,25$