Question

Спростити вираз 1) 2) 3)

Answer 1

$\frac{(1-sin \alpha )(1+sin \alpha )}{sin^2 \alpha }=\frac{1-sin^2 \alpha }{sin^2 \alpha }=\frac{cos^2 \alpha }{sin^2 \alpha }=ctg^2 \alpha \\\\2)\; cos \alpha -cos \alpha \cdot sin^2 \alpha =cos \alpha (1-sin^2 \alpha )=cos \alpha \cdot cos^2 \alpha =cos^3 \alpha \\\\3)\; tg \alpha \cdot ctg \alpha -cos^2 \alpha =1-cos^2 \alpha =sin^2 \alpha$

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