Question

\frac{1-cos}{sen} +\frac{sen}{1-cos} =2cos [/tex]

Answer 1

Obtengo algo ligeramente distinto, tal vez hay un error tipografico por ahi.

$\frac{1-Cos(x)}{Sin(x)}+\frac{Sin(x)}{1-Cos(x)}=\frac{[(1-Cos(x))(1-Cos(x))]+[(Sin(x))(Sin(x))]}{(Sin(x))(1-Cos(x))}$

$=\frac{[(1-Cos(x))^{2}]+[Sin^{2}(x)]}{(Sin(x))(1-Cos(x))}=\frac{(1-2Cos(x)+Cos^{2}(x))+[Sin^{2}(x)]}{(Sin(x))(1-Cos(x))}$

$=\frac{1-2Cos(x)+Cos^{2}(x)+Sin^{2}(x)}{(Sin(x))(1-Cos(x))} =\frac{1-2Cos(x)+1}{(Sin(x))(1-Cos(x))}$

$=\frac{2(1-Cos(x))}{(Sin(x))(1-Cos(x))}=\frac{2}{Sin(x)}=2Csc(x)$