Question

Помогите!!! Даю 100 баллов за полное решение с объяснением.

Answer 1

Объяснение:

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

$4)\\sin^2\alpha +cos^2\alpha *(1+ctg^2\alpha )*sin^2\alpha =sin^2\alpha +cos^2\alpha *(1+\frac{cos^2\alpha }{sin^2\alpha } )*sin^2\alpha =\\=sin^2\alpha +cos^2\alpha *\frac{sin^2+cos^2\alpha }{sin^2\alpha } *sin^2\alpha =sin^2\alpha +cos^2\alpha *\frac{1}{sin^2\alpha }*sin^2\alpha =\\=sin^2\alpha +cos^2\alpha =1.$