Question

Tìm các nghiệm của phươn trình 

\(\sqrt{2}cos\left(x+\dfrac{\pi}{3}\right)=1\) trên \(\left[0;2\pi\right]\)

Answer 1

\(\sqrt{2}cos\left(x+\dfrac{\pi}{3}\right)=1\)

\(\Leftrightarrow cos\left(x+\dfrac{\pi}{3}\right)=\dfrac{1}{\sqrt{2}}\)

\(\Leftrightarrow x+\dfrac{\pi}{3}=\pm\dfrac{\pi}{4}+k2\pi\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{\pi}{12}+k2\pi\\x=-\dfrac{7\pi}{12}+k2\pi\end{matrix}\right.\)

\(0\le-\dfrac{\pi}{12}+k2\pi\le2\pi\Leftrightarrow...\)

\(0\le-\dfrac{7\pi}{12}+k2\pi\le2\pi\Leftrightarrow...\)