(sin^4 a - cos^4 a + cos^2a) / (2*(1-cosa))

[latex]\frac{\sin^4 \alpha -\cos^4 \alpha +\cos2 \alpha }{2(1-\cos \alpha )}=\frac{\sin^4 \alpha -\cos^4 \alpha +\cos^2 \alpha-\sin^2 \alpha }{2(1-\cos \alpha )}=\\\\=\frac{\sin^2 \alpha (\sin^2 \alpha -1)+\cos^2 \alpha (1-\cos^2 \alpha )}{2(1-\cos \alpha )}=\frac{\sin^2 \alpha (\sin^2 \alpha -1)+\cos^2 \alpha \sin^2 \alpha }{2(1-\cos \alpha )}=\\\\=\frac{\sin^2 \alpha (\sin^2 \alpha -1+\cos^2 \alpha)}{2(1-\cos \alpha )}=\frac{\sin^2 \alpha (1 -1)}{2(1-\cos \alpha )}=0.[/latex]