Question

докажите ,что уравнение правильно

Answer 1

$(sin alpha +cos alpha )^2+(sin alpha -cos alpha )^2=2 \ sin^2 alpha +2sin alpha cos alpha +cos^ {2} alpha +sin^2-2sin alpha cos alpha +cos^2 alpha = \ =sin^2 alpha +cos^2 alpha +sin^2 alpha +cos^2 alpha=1+1=2$

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