[tex]4\cos ^2x+1=2[/tex]
Subtract 1 from both sides
[tex]\begin{gathered} 4\cos ^2x+1-1=2-1 \\ 4\cos ^2x=1 \end{gathered}[/tex]
Divide both sides by 4
[tex]\begin{gathered} \frac{4cos^2x}{4}=\frac{1}{4} \\ \cos ^2x=\frac{1}{4} \end{gathered}[/tex]
Now, we will take square root for both sides to find cos x
[tex]\begin{gathered} \cos x=\sqrt[]{\frac{1}{4}} \\ \cos x=\frac{1}{2};\cos x=-\frac{1}{2} \end{gathered}[/tex]
Square root give two answers, one + and the other -
Now we will find the angles which have cos = 1/2 or -1/2
[tex]\begin{gathered} x=\cos ^{-1}(\frac{1}{2}) \\ x=\frac{\pi}{3} \end{gathered}[/tex]
The answer is C
