Срочно нужно! Помогите пожалуйста!

Решите задачу:

$cos^2(a)+\frac{sin(\frac{\pi}{2}+a)*cos(\pi-a)}{ctg(\pi-a)*tg(\frac{3\pi}{2}-a)}=\\\\ =cos^2(a)+\frac{cos(a)*[-cos(a)]}{-ctg(a)*ctg(a)}=\\\\ =cos^2(a)+\frac{cos^2(a)}{ctg^2(a)}=\\\\ =cos^2(a)+cos^2(a):ctg^2(a)=\\\\ =cos^2(a)+cos^2(a):\frac{cos^2(a)}{sin^2(a)}=\\\\ =cos^2(a)+cos^2(a)*\frac{sin^2(a)}{cos^2(a)}=\\\\ =cos^2(a)+sin^2(a)=1$