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