[tex](sin\alpha+cos\alpha)^2=sin^2\alpha+2sin\alpha cos\alpha+cos^2\alpha\\\\(sin\alpha+cos\alpha)^2=1+2sin\alpha cos\alpha\\\\(sin\alpha+cos\alpha)^2=1+2\cdot\frac{3}{8}\\\\(sin\alpha+cos\alpha)^2=1+\frac{3}{4}\\\\(sin\alpha+cos\alpha)^2=\frac{7}{4}\\\\sin\alpha+cos\alpha=\sqrt{\frac{7}{4}}\\\\sin\alpha+cos\alpha=\frac{\sqrt7}{2}[/tex]
