Question

Помогите, пожалуйста, с решением

Answer 1

$Cos^{2}\alpha-Cos(\alpha+\frac{\pi }{6})Cos(\alpha-\frac{\pi }{6})=Cos^{2}\alpha-\frac{1}{2}(Cos(\alpha+\frac{\pi }{6}+\alpha-\frac{\pi }{6})+Cos(\alpha+\frac{\pi }{6}-\alpha+\frac{\pi }{6}))=Cos^{2}\alpha-\frac{1}{2}(Cos2\alpha+Cos\frac{\pi }{3})=Cos^{2}\alpha-\frac{1}{2}Cos2\alpha-\frac{1}{2}*Cos\frac{\pi }{3}=Cos^{2}\alpha-\frac{1}{2}(2Cos^{2}\alpha} -1)-\frac{1}{2}*\frac{1}{2}=Cos^{2}\alpha -Cos^{2} \alpha+\frac{1}{2}-\frac{1}{4}=\frac{1}{4}=0,25$