Nếu \(\cos \alpha  + \sin \alpha  = \sqrt 2 \,\,\,\left( {0...

* Hướng dẫn giải

\(\begin{array}{l}
\cos \alpha  + \sin \alpha  = \sqrt 2 \, \Leftrightarrow \sqrt 2 \sin \left( {\alpha  + \frac{\pi }{4}} \right) = \sqrt 2 \\
 \Leftrightarrow \sin \left( {\alpha  + \frac{\pi }{4}} \right) = 1 \Leftrightarrow \alpha  + \frac{\pi }{4} = \frac{\pi }{2}\left( {0 < \alpha  < \frac{\pi }{2}} \right)\\
 \Leftrightarrow \alpha  = \frac{\pi }{4}
\end{array}\)