Question

tg(-t)/tgt+ctgt=-sin^2t доказать тождество

Answer 1

$frac{tg(-t)}{tgt+ctgt}= frac{-tgt}{ frac{sint}{cost}+ frac{cost}{sint} } = frac{-tgt}{ frac{sintcdot sint+costcdot cost}{costcdot sint}} }= \ =-tgt cdot costcdot sint = frac{-sint}{cost} cdot costcdot sint =-sin ^{2}t$