Объяснение:

[tex]\frac{cos^2(\pi +\alpha )-sin^2(\frac{\pi }{2}+\alpha )-cos(\pi -\alpha )*cos(2\pi +\alpha ) }{tg^2(\frac{\pi }{2}+\alpha )*vtg(\frac{3\pi }{2}-\alpha ) } =\frac{(-cos\alpha )^2-(cos\alpha )^2-(-cos\alpha )*cos\alpha }{(-ctg\alpha )^2*(-tg\alpha )^2}=\\[/tex]

[tex]=\frac{cos^2\alpha -cos^2\alpha +cos^2\alpha }{ctg^2\alpha*tg^2\alpha } =\frac{cos^2\alpha }{(ctg\alpha *tg\alpha )^2}=\frac{cos^2\alpha }{1^2} =\frac{cos^2\alpha }{1}=cos^2\alpha .[/tex]