Question

A. 0b. pi/6c. pi/3d. pi/2Which of the following is a solution for the equation.

Answer 1

`4\cos ^2x+1=2`

Subtract 1 from both sides

`\begin{gathered} 4\cos ^2x+1-1=2-1 \\ 4\cos ^2x=1 \end{gathered}`

Divide both sides by 4

`\begin{gathered} (4cos^2x)/(4)=(1)/(4) \\ \cos ^2x=(1)/(4) \end{gathered}`

Now, we will take square root for both sides to find cos x

`\begin{gathered} \cos x=\sqrt[]{(1)/(4)} \\ \cos x=(1)/(2);\cos x=-(1)/(2) \end{gathered}`

Square root give two answers, one + and the other -

Now we will find the angles which have cos = 1/2 or -1/2

`\begin{gathered} x=\cos ^(-1)((1)/(2)) \\ x=(\pi)/(3) \end{gathered}`

The answer is C