Answer
If $2\sin x\cos x+\sqrt{2}\cos x=0$, then $\underline{\cos x\,}=0$ or $\underline{2\sin x+\sqrt{2}}=0$.
Work Step by Step
To evaluate the values, find out the common numbers:
$\begin{align}
& 2\sin x\cos x+\sqrt{2}\cos x=0 \\
& \cos x\left( 2\sin x+\sqrt{2} \right)=0 \\
& \cos x=0 \\
& 2\sin x+\sqrt{2}=0
\end{align}$
So, the values will be $2\sin x+\sqrt{2}=0$ and $\cos x=0$.
