Question

Упростить выражение: ctg^2aльфа - cos^2aльфа

Answer 1

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