Question

tgx/1+tg^2x + ctgx/1+ctg^2x

Answer 1

$\frac{tgx}{1+tg ^{2}x } + \frac{Ctgx}{1+Ctg ^{2}x } = \frac{tgx}{ \frac{1}{Cos ^{2}x } }+ \frac{Ctgx}{ \frac{1}{Sin ^{2}x } }= \frac{Sinx*Cos ^{2} x}{Cosx}+ \frac{Cosx*Sin ^{2}x }{Sinx} =$$SinxCosx + SinxCosx = 2SinxCosx = Sin2x$