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Solve for the exact solutions in the interval
[0,2pi). If it has no solutions, respond with DNE.

8sec^(2)((x)/(2))=4

Solve for the exact solutions in the interval $[0,2 \pi)$ . If it has no solutions, respond with DNE. $\newline$ $8 \sec ^{2}\left(\frac{x}{2}\right)=4$

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Full solution

Q. Solve for the exact solutions in the interval

[0,2 \pi)

. If it has no solutions, respond with DNE.

\newline

8 \sec ^{2}\left(\frac{x}{2}\right)=4

Simplify Equation: Simplify the given equation: $\newline$ $8\sec^2(\frac{x}{2}) = 4$ $\newline$ Divide both sides by $8$ : $\newline$ $\sec^2(\frac{x}{2}) = \frac{1}{2}$
Divide by $8$ : Convert $\sec^2$ to $\cos^2$ : $\newline$ $\sec^2(\frac{x}{2}) = \frac{1}{\cos^2(\frac{x}{2})}$ $\newline$ $\frac{1}{\cos^2(\frac{x}{2})} = \frac{1}{2}$ $\newline$ $\cos^2(\frac{x}{2}) = 2$

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