Упростите выражение: 2cos^2 альфа/2-cosальфа-1

[latex]2Cos^{2}\frac{a}{2} - Cosa - 1 = 2Cos^{2}\frac{a}{2} - Cos2\frac{a}{2} - 1 = [/latex] [latex]2Cos^{2}\frac{a}{2} - (Cos^{2}\frac{a}{2} - Sin^{2}\frac{a}{2}) - 1 = 2Cos^{2}\frac{a}{2} - Cos^{2}\frac{a}{2} + Sin^{2}\frac{a}{2} - 1 = [/latex] [latex]Cos^{2}\frac{a}{2} + Sin^{2}\frac{a}{2} - 1 = 1 - 1 = 0[/latex]