Question

Solve the multiple-angle equation. (Enter your answers as a comma-separated list. Use n as an arbitrary integer. Enter your response in radians.)2 cos 2x − 1 = 0

Answer 1

Given:

The function is:

`2\cos2x-1=0`

Find-:

The value of "x"

Explanation-:

The value of x is:

`\begin{gathered} 2\cos2x-1=0 \\ \\ 2\cos2x=1 \\ \\ \cos2x=(1)/(2) \\ \end{gathered}`

Solve for x is:

`\begin{gathered} \cos2x=(1)/(2) \\ \\ 2x=\cos^(-1)((1)/(2)) \\ \\ 2x=(\pi)/(3)+2\pi n\text{ and }2x=(5\pi)/(3)+2\pi n \end{gathered}`

The value of "x" is:

`\begin{gathered} 2x=(\pi)/(3)+2\pi n \\ \\ x=(\pi)/(2*3)+(2\pi n)/(2) \\ \\ x=(\pi)/(6)+\pi n \end{gathered}`

Another value of "x" is:

`\begin{gathered} 2x=(5\pi)/(3)+2\pi n \\ \\ x=(5\pi)/(3*2)+(2\pi n)/(2) \\ \\ x=(5\pi)/(6)+\pi n \end{gathered}`

So, the answer is:

`x=(\pi)/(6)+\pi n,(5\pi)/(6)+\pi n`