Đáp án:
$\begin{array}{l}
\sqrt 2 .\sin \left( {x + \frac{\pi }{4}} \right)\\
= \sqrt 2 .\left( {{\mathop{\rm s}\nolimits} {\rm{inx}}.\cos \frac{\pi }{4} + \cos x.\sin \frac{\pi }{4}} \right)\\
= \sqrt 2 .\left( {\sin x.\frac{1}{{\sqrt 2 }} + {\mathop{\rm cosx}\nolimits} .\frac{1}{{\sqrt 2 }}} \right)\\
= \sin x + \cos x\\
Vậy\,\sin x + \cos x = \sqrt 2 .\sin \left( {x + \frac{\pi }{4}} \right)
\end{array}$
