Question

Nghiệm của phương trình \(sinx+\sqrt{3}cosx=\sqrt{2}\) là?

 

Answer 1

\(\Leftrightarrow\dfrac{1}{2}sinx+\dfrac{\sqrt{3}}{2}cosx=\dfrac{\sqrt{2}}{2}\)

\(\Leftrightarrow sin\left(x+\dfrac{\pi}{3}\right)=\dfrac{\sqrt{2}}{2}\)

\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{\pi}{3}=\dfrac{\pi}{4}+k2\pi\\x+\dfrac{\pi}{3}=\dfrac{3\pi}{4}+k2\pi\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{\pi}{12}+k2\pi\\x=\dfrac{5\pi}{12}+k2\pi\end{matrix}\right.\)