[tex]\frac{sin\alpha-cos\alpha}{sin\alpha+cos\alpha}+\frac{sin\alpha+cos\alpha}{sin\alpha-cos\alpha}=\\\frac{(sin\alpha-cos\alpha)(sin\alpha-cos\alpha)}{(sin\alpha+cos\alpha)(sin\alpha-cos\alpha)}+\frac{(sin\alpha+cos\alpha)(sin\alpha+cos\alpha)}{(sin\alpha+cos\alpha)(sin\alpha-cos\alpha)}=\\\frac{(sin\alpha-cos\alpha)^2}{sin^2\alpha-cos^2\alpha}+\frac{(sin\alpha+cos\alpha)^2}{sin^2\alpha-cos^2\alpha}=[/tex]
[tex]\frac{sin^2\alpha-2sin\alpha cos\alpha+cos^2\alpha}{sin^2\alpha-cos^2\alpha}+\frac{sin^2\alpha+2sin\alpha cos\alpha + cos^2\alpha}{sin^2\alpha-cos^2\alpha}=\\\frac{sin^2\alpha-2sin\alpha cos\alpha + cos^2\alpha + sin^2\alpha + 2sin\alpha cos\alpha + cos^2\alpha}{sin^2\alpha-cos^2\alpha}=[/tex]
[tex]\frac{2sin^2\alpha+2cos^2\alpha}{sin^2\alpha-cos^2\alpha}=\\\frac{2(sin^2\alpha+cos^2\alpha)}{sin^2\alpha-cos^2\alpha}=\\\frac{2*1}{sin^2\alpha-cos^2\alpha}=\\\frac{2}{sin^2\alpha-cos^2\alpha}[/tex]