Question

298 Пожалуйста помогите!

Answer 1

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