Given:
There are given the equation:
[tex]cos2x+cosx=0[/tex]
Explanation:
According to the question:
We need to find the value where the given equation is satisfied.
So,
From the equation:
Put the 0 for x for the option first.
[tex]\begin{gathered} cos2x+cosx=0 \\ cos2(0)+cos(0)=0 \\ 1+1=0 \\ 2\ne0 \end{gathered}[/tex]
Then,
For the second option:
[tex]\begin{gathered} cos2x+cosx=0 \\ cos2(\frac{\pi}{3})+cos\frac{\pi}{3}\ne0 \end{gathered}[/tex]
For option third:
[tex]\begin{gathered} cos2x+cosx=0 \\ cos2(\pi)+cos(\pi)=0 \\ -1+2cos^2(\pi)+cos(\pi)=0 \\ -1+2(-1)^2-1=0 \\ -1+2-1=0 \\ 0=0 \end{gathered}[/tex]
Final answer:
Hence, the correct option C.
