Объяснение:

[tex]sin^2\alpha +cos(\frac{\pi }{3}-\alpha )*cos(\frac{\pi }{3}+\alpha )=\\=sin^2\alpha +(sin \frac{\pi }{3}*cos\alpha -sin\alpha *cos\frac{\pi }{3})*(sin\frac{\pi }{3}*cos\alpha +sin\alpha* cos\frac{\pi }{3} )=\\=sin^2\alpha +(\frac{\sqrt{3} }{2}*cos\alpha -\frac{1 }{2}*sin\alpha )*(\frac{\sqrt{3} }{2}*cos\alpha +\frac{1}{2}*sin\alpha )=\\ =sin^2\alpha +(\frac{\sqrt{3} }{2}*cos\alpha )^2-(\frac{1}{2}*sin^2\alpha )^2=sin^2\alpha +\frac{3}{4} *cos^2\alpha -\frac{1}{4}*sin^2\alpha =\\[/tex]

[tex]=\frac{3}{4} *sin^2\alpha +\frac{3}{4}*cos^2\alpha =\frac{3}{4} *(sin^2\alpha +cos^2\alpha )=\frac{3}{4}*1=\frac{3}{4}.[/tex]

Ответ: 3/4.