Question

Помогите доказать тождество

Answer 1

$1)1-cos^2 alpha =sin^2 alpha \ \ 2) frac{1-cos^2 alpha }{sin alpha* cos alpha }= frac{sin^2 alpha }{sin alpha* cos alpha} = frac{sin alpha }{cos alpha } =tg alpha \ \ 3)tg alpha +ctg alpha = frac{sin alpha }{cos alpha } + frac{cos alpha }{sin alpha } = frac{sin^2 alpha +cos^2 alpha }{sin alpha* cos alpha } = frac{1}{sin alpha* cos alpha}$

$4)sin^2 alpha * frac{1}{sin alpha *cos alpha } = frac{sin alpha }{cos alpha } =tg alpha$

$frac{1-cos^2 alpha }{sin alpha* cos alpha } -sin^2 alpha (tg alpha +ctg alpha )=0 \ \ frac{sin^2 alpha }{sin alpha* cos alpha} -sin^2 alpha * frac{1}{sin alpha* cos alpha} =0 \ \ frac{sin alpha }{cos alpha } - frac{sin alpha }{cos alpha } =0 \ 0=0$

Answer 2

sin²α/(sinαcosα)-sin²α((sin²α+cos²α)/cosαsinα)=0
sin²α/(sinαcosα)-sin²α/(sinαcosα)=0
0=0-верно