Question

$frac{1-2sin^{2} alpha}{1+sin2 alpha }, tg alpha = -5$

Answer 1

$tg alpha =-5\\ frac{1-2sin^2 alpha }{1+sin2 alpha } = frac{cos2 alpha }{sin^2 alpha +cos^2 alpha +2sin alpha cdot cos alpha } = frac{cos^2 alpha -sin^2 alpha }{(cos alpha +sin alpha )^2} =\\= frac{(cos alpha -sin alpha )(cos alpha +sin alpha )}{(cos alpha +sin alpha )^2} =frac{cos alpha -sin alpha }{cos alpha +sin alpha }=[, frac{:cos alpha }{:cos alpha }, ]=\\= frac{1-tg alpha }{1+tg alpha }=frac{1+5}{1-5}=-frac{6}{4}=-frac{3}{2}=-1,5$

Answer 2

решение смотри на фотографии