Question

упростите выражение ((sina-cosa)^2 - 1) (1+tg^2a) + 2ctg( п/2 - a)

Answer 1

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