Упростите выражение
cos²(α-π/6)+cos²(α+π/6)+sin²α

[tex]cos^2(a-\frac{\pi}{6})+cos^2(a+\frac{\pi}{6})+sin^2a=\\\\= \frac{1+cos(2a-\frac{\pi}{3})}{2} +\frac{1+cos(2a+\frac{\pi}{3})}{2}+\frac{1-cos2a}{2}=\\\\= \frac{1}{2}\cdot (3+\underbrace {cos(2a-\frac{\pi}{3})+cos(2a+\frac{\pi}{3})}-cos2a)=\\\\=\frac{1}{2}\cdot (3+2\cdot cos2a\cdot cos(-\frac{\pi}{3})-cos2a)=\\\\=\frac{1}{2}\cdot (3+2\cdot \frac{\sqrt3}{2}\cdot cos2a-cos2a)=\frac{1}{2}\cdot (3+(\sqrt3-1)\cdot cos2a)=\\\\=\frac{3}{2}+\frac{\sqrt3-1}{2}\cdot cos2a[/tex]