Question

tg t *Cos^2 t = (tg t + ctg t )^-1

Answer 1

$tgt*cos^2t=frac{1}{tgt+ctgt}\tgt*cos^2t=frac{1}{frac{sint}{cost}+frac{cost}{sint}}\tgt*cos^2t=frac{1}{frac{1}{sintcost}}\frac{sint}{cost}*cos^2t=sintcost\sintcost=sintcost$