Verified answer

[tex]\displaystyle\bf\\\frac{Cos^{2} (\pi +\alpha )+Sin^{2}(\frac{\pi }{2} -\alpha )-Cos(\pi -\alpha )Cos(2\pi -\alpha ) }{tg^{2}(\frac{\pi }{2} -\alpha ) Ctg^{2}(\frac{3\pi }{2} -\alpha)} =\\\\\\=\frac{Cos^{2} \alpha +Cos^{2}\alpha -(-Cos\alpha )\cdot Cos\alpha }{Ctg^{2}\alpha \cdot tg^{2} \alpha } =\frac{Cos^{2} \alpha +Cos^{2}\alpha +Cos^{2} \alpha }{1} =3Cos^{2} \alpha \\\\\\3Cos^{2} \alpha =3Cos^{2} \alpha[/tex]

Что и требовалось доказать