Question

Cos(x+1)+cos2x=0

Answer 1

\(cos\left(x+1\right)+cos2x=0\)

\(\Leftrightarrow2cos\left(x+\dfrac{1}{2}\right).cos\left(\dfrac{1}{2}-\dfrac{x}{2}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}cos\left(x+\dfrac{1}{2}\right)=0\\cos\left(\dfrac{1}{2}-\dfrac{x}{2}\right)=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{1}{2}=\dfrac{\pi}{2}+k\pi\\\dfrac{1}{2}-\dfrac{x}{2}=\dfrac{\pi}{2}+k\pi\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{2}-\dfrac{1}{2}+k\pi\\x=1-\pi+k2\pi\end{matrix}\right.\)