Question

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

Answer 1

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