Cho sin alpha+cos alpha=4/3, pi/2

* Hướng dẫn giải

$\sin \alpha +\cos \alpha =\frac{3}{4}\to \cos \alpha =\frac{3}{4}-\sin \alpha$

Lại có: ${\sin }^2\alpha +{\cos }^2\alpha =1$

$\Rightarrow {\sin }^2\alpha +{\left(\frac{3}{4}-\sin \alpha \right)}^2=1$

$\Rightarrow 2{\sin }^2\alpha -\frac{3}{2}\sin \alpha -\frac{7}{16}=0$