Đáp án:
\( \Leftrightarrow \left\{\begin{matrix} x=\frac{-\pi}{6}+k.2\pi
& & \\ x=\frac{\pi}{2}+k2\pi
& &
\end{matrix}\right. \)
Giải thích các bước giải:
\(sinx+\sqrt{3}cosx=1\)
\( \Leftrightarrow 2(\frac{1}{2}sinx+\frac{\sqrt{3}}{2}cosx)=1 \)
\( \Leftrightarrow 2.sin(x+\frac{\pi}{3})=\frac{1}{2}\)
\( \Leftrightarrow sin(x+\frac{\pi}{3})=\frac{1}{2} \)
\( \Leftrightarrow \left\{\begin{matrix} x=\frac{-\pi}{6}+k.2\pi
& & \\ x=\frac{\pi}{2}+k2\pi
& &
\end{matrix}\right. \)
