Доказать тождество: sina/1+cosa + 1+cosa/sina = 2/sina

[latex] \frac{sin(a)}{1+cos(a)} + \frac{1+cos(a)}{sin(a)} = \frac{2}{sin(a)} [/latex] [latex] \frac{sin^2(a) + (1+cos(a))^2}{sin(a)(1+cos(a)} = \frac{sin^2(a) + 1 + 2cos(a) + cos^2(a)}{sin(a)(1+cos(a)} = \frac{2+2cos(a)}{sin(a)(1+cos(a)} = [/latex] [latex]\frac{2(1+1cos(a))}{sin(a)(1+cos(a)} = \frac{2}{sin(a)} [/latex] Что и требовалось доказать