Sin(a-π)+cos(a-3π/2)/ctg(a-π/2)-tg(π+2)

[latex]\frac{\sin(\alpha-\pi)+\cos(\alpha-\frac{3\pi}2)}{ctg(\alpha-\frac\pi2)-tg(\pi+\alpha)}=\frac{-\sin(\pi-\alpha)+\cos(\frac{3\pi}2-\alpha)}{-ctg(\frac\pi2-\alpha)-tg(\pi+\alpha)}=\frac{-\sin\alpha-\sin\alpha}{-tg\alpha-tg\alpha}=\\=\frac{-2\sin\alpha}{-2tg\alpha}=\frac{\sin\alpha}{tg\alpha}=\frac{\sin\alpha\cos\alpha}{\sin\alpha}=\cos\alpha[/latex]