(1+tg^2альфа)cos^2альфа-1.

[latex](1+\tan^2 \alpha )\cdot\cos^2 \alpha -1=\bigg(1+ \dfrac{\sin^2 \alpha }{\cos^2 \alpha } \bigg)\cdot\cos^2 \alpha -1=\\\\= \dfrac{(\cos^2 \alpha +\sin^2 \alpha )}{\cos^2 \alpha }\cdot\cos^2 \alpha -1=\cos^2 \alpha +\sin^2 \alpha -1=1-1=0[/latex]