Question

Помогите упростить выражения

Answer 1

1) $ctg(a)+ frac{sin(a)}{1+cos(a)} = frac{cos(a)}{sin(a)} +frac{sin(a)}{1+cos(a)}= frac{cos(a)(1+cos(a))+sin^2(a)}{sin(a)(1+cos(a))}=$
$=frac{cos(a)+cos^2(a)+sin^2(a)}{sin(a)(1+cos(a))}= frac{cos(a)+1}{sin(a)(1+cos(a))} = frac{1}{sin(a)}$

2) $frac{2-sin^2(a)-cos^2(a)}{2+sin^2(a)+cos^2(a)} = frac{2-1}{2+1} = frac{1}{3}$

3) $frac{ctg( pi -a)}{sin( pi +a)} * frac{cos(3 pi /2+a)}{ctg(3 pi /2+a)} = frac{-ctg(a)}{-sin(a)}* frac{sin(a)}{-tg(a)}= - frac{ctg(a)}{tg(a)} =-ctg^2(a)$

4) $frac{sin(-a)*ctg(-a)}{cos(360-a)*tg(180+a)} = frac{-sin(a)*(-cos(a))/sin(a)}{cos(a)*sin(a)/cos(a)}= frac{cos(a)}{sin(a)}=tg(a)$