Answer: option d.
Step-by-step explanation:
Based on the information given in the problem, you know that:
[tex]tan^2x=\frac{1}{2}[/tex]
You also know that:
[tex]sec^2(x)=tan^2(x)+1[/tex]
Substitute values. Then, you obtain:
[tex]sec^2(x)=\frac{1}{2}+1\\\\sec^2(x)=\frac{3}{2}[/tex]
Apply square root to both sides. Therefore, you obtain:
[tex]\sqrt{sec^2(x)}=\±\sqrt{\frac{3}{2}}\\\\sec(x)=\±\frac{\sqrt{3}}{\sqrt{2}}\\\\sec(x)=\±\frac{\sqrt{3}}{\sqrt{2}}\frac{\sqrt{2}}{\sqrt{2}}\\\\sec(x)=\±\frac{\sqrt{3(2)}}{2}\\\\sec(x)=\±\frac{\sqrt{6}}{2}[/tex]
