Câu hỏi 9

\(\sin x+\cos x=1\Leftrightarrow \sqrt{2}\sin \left( x+\dfrac{\pi }{4} \right)=1\Leftrightarrow \sin \left( x+\dfrac{\pi }{4} \right)=\dfrac{1}{\sqrt{2}}\)

\( \Leftrightarrow \left[ \matrix{
x + {\pi \over 4} = {\pi \over 4} + k2\pi \hfill \cr
x + {\pi \over 4} = {{3\pi } \over 4} + k2\pi \hfill \cr} \right. \Leftrightarrow \left[ \matrix{
x = k2\pi \hfill \cr
x = {\pi \over 2} + k2\pi \hfill \cr} \right.\,\,\left( {k \in } \right)\)

Chọn C.