Question

докажите тождество
tg t * cos^2 t = (tg t +ctg t)^-1

Answer 1

$tg t cos^2 t = frac{sint}{cost} cdot cos^2 t =sintcos t \ (tg t +ctg t)^{-1}=( frac{sint}{cost} + frac{cost}{sint} )^{-1}= ( frac{sin^2+cos^2t}{sintcost} )^{-1}= \ =( frac{1}{sintcost} )^{-1}=sintcost \ tg t cos^2 t =(tg t +ctg t)^{-1}$