Question

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

Answer 1

$frac{sin(alpha-pi)+cos(alpha-frac{3pi}2)}{ctg(alpha-fracpi2)-tg(pi+alpha)}=frac{-sin(pi-alpha)+cos(frac{3pi}2-alpha)}{-ctg(fracpi2-alpha)-tg(pi+alpha)}=frac{-sinalpha-sinalpha}{-tgalpha-tgalpha}=\=frac{-2sinalpha}{-2tgalpha}=frac{sinalpha}{tgalpha}=frac{sinalphacosalpha}{sinalpha}=cosalpha$