[tex](sin \alpha - cos \alpha)^2=\frac{1}{5}\\\\sin^2\alpha-2ain\alpha cos\alpha+cos^2\alpha=\frac{1}{5}\\\\1-2sin\alpha cos\alpha=\frac{1}{5}\\\\-2sin\alpha cos\alpha=\frac{1}{5}-1\\\\-2sin\alpha cos\alpha=-\frac{4}{5}\ \ \ |:(-1)\\\\ 2sin\alpha cos\alpha=\frac{4}{5}[/tex]
[tex](sin\alpha+cos\alpha)^2=sin^2\alpha+2sin\alpha cos\alpha+cos^2\alpha=1+2sin\alpha cos\alpha=1+\frac{4}{5}=1\frac{4}{5}=\frac{9}{5}[/tex]
