Question

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

Answer 1

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