Question

Упростить выражение ctg^2a-cos^2a=

Answer 1

${\rm ctg}^2\alpha-\cos^2\alpha=\cos^2\alpha\left(\dfrac{1}{\sin^2\alpha}-1\right)=\cos^2\alpha\cdot \dfrac{1-\sin^2\alpha}{\sin^2\alpha}=\\ \\ \\ =\cos^2\alpha\cdot \dfrac{\cos^2\alpha}{\sin^2\alpha}=\cos^2\alpha\cdot {\rm ctg}^2\alpha$