Question

298 Пожалуйста помогите!

Answer 1

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