Question

Which of the following isn’t a solution to cos 2x + cos x=0 on the interval [0,2pi)

Answer 1

Given:

There are given the equation:

`cos2x+cosx=0`

Step-by-step 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.

`\begin{gathered} cos2x+cosx=0 \\ cos2(0)+cos(0)=0 \\ 1+1=0 \\ 2\\e0 \end{gathered}`

Then,

For the second option:

`\begin{gathered} cos2x+cosx=0 \\ cos2((\pi)/(3))+cos(\pi)/(3)\\e0 \end{gathered}`

For option third:

`\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}`

Final answer:

Hence, the correct option C.