Answer
No solution.
Work Step by Step
We have to solve the equation on the interval $[0,2\pi )$; follow the course of action given below:
$\begin{align}
& 4{{\sec }^{2}}x-2=0 \\
& 4{{\sec }^{2}}x=0+2 \\
& {{\sec }^{2}}x=\frac{2}{4} \\
& {{\sec }^{2}}x=\frac{1}{2}
\end{align}$
And the above expression can be further simplified as:
$\begin{align}
& \frac{1}{{{\cos }^{2}}x}=\frac{1}{2} \\
& \text{co}{{\text{s}}^{2}}x=2 \\
& \cos x=\pm \sqrt{2}
\end{align}$
The value of $\cos x$ cannot exceed 1.
In this expression $\cos x=\pm \sqrt{2}$. Hence, it will not be a part of the solution.
