Hướng dẫn giải:

Chọn đáp án C

Ta có $\frac{1}{\sqrt{2}}\sin \alpha +\sin \left( \frac{\pi }{2}-\alpha  \right)=1\Leftrightarrow \sin \alpha +\sqrt{2}\cos \alpha =\sqrt{2}\Leftrightarrow \sin \alpha =\sqrt{2}-\sqrt{2}\cos \alpha $

$\Leftrightarrow {{\sin }^{2}}\alpha =2{{\cos }^{2}}\alpha -4\cos \alpha +2\Leftrightarrow 3{{\cos }^{2}}\alpha -4\cos \alpha +1=0\Leftrightarrow \left[ \begin{align}& \cos \alpha =1\left( l \right) \\  & \cos \alpha=\frac{1}{3}\Rightarrow \sin \alpha =\frac{2\sqrt{2}}{3} \\ \end{align} \right.$