Упростить вырожение 1 / tga + Sina / 1 + cos a

Решите задачу:

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