Question

$\frac{ct}{tg+ctg}$

Answer 1

$\frac{ctg \alpha }{tg \alpha +ctg \alpha } = \frac{ \frac{1}{tg \alpha } }{tg \alpha +\frac{1}{tg \alpha } } =\frac{ 1 }{tg \alpha (tg \alpha +\frac{1}{tg \alpha })}=\frac{ 1 }{tg^2 \alpha +1}=\frac{ 1 }{\frac{1}{\cos^2 \alpha }}=\cos^2 \alpha.$