Question

(1+Ctg2a*ctga)/(Tga+ctga)

Answer 1

$\frac{1+Ctg2 \alpha *Ctg \alpha }{tg \alpha +Ctg \alpha }= \frac{1+ \frac{Ctg ^{2} \alpha -1 }{2Ctg \alpha }*Ctg \alpha }{ \frac{1}{Ctg \alpha }+Ctg \alpha }=[tex] \frac{ \frac{2+Ctg ^{2} \alpha -1 }{2} }{ \frac{1+Ctg ^{2} \alpha }{Ctg \alpha } } = \frac{(1+Ctg ^{2} \alpha)*Ctg \alpha }{2*(1+Ctg ^{2} \alpha ) }= \frac{1}{2}Ctg \alpha$