Question

Find sec x if tan^2 x= 1/2 (picture provided)

Answer 1

Answer:

D

Step-by-step explanation:

Answer 2

Answer: option d.

Step-by-step explanation:

Based on the information given in the problem, you know that:

$tan^2x=\frac{1}{2}$

You also know that:

$sec^2(x)=tan^2(x)+1$

Substitute values. Then, you obtain:

$sec^2(x)=\frac{1}{2}+1\\\\sec^2(x)=\frac{3}{2}$

Apply square root to both sides. Therefore, you obtain:

$\sqrt{sec^2(x)}=\±\sqrt{\frac{3}{2}}\\\\sec(x)=\±\frac{\sqrt{3}}{\sqrt{2}}\\\\sec(x)=\±\frac{\sqrt{3}}{\sqrt{2}}\frac{\sqrt{2}}{\sqrt{2}}\\\\sec(x)=\±\frac{\sqrt{3(2)}}{2}\\\\sec(x)=\±\frac{\sqrt{6}}{2}$