Given that the values of sin x and cos x are [tex]\sin x=\frac{1}{2}[/tex] and [tex]\cos x=\frac{\sqrt{3}}{2}[/tex]
We need to determine the value of tan x.
The value of tan x:
Using the trigonometric identity, the formula for tan x is given by
[tex]tan \ x=\frac{sin \ x}{cos \ x}[/tex]
Now, substituting the values [tex]\sin x=\frac{1}{2}[/tex] and [tex]\cos x=\frac{\sqrt{3}}{2}[/tex] in the above formula, we get;
[tex]tan \ x=\frac{(\frac{1}{2})}{(\frac{\sqrt{3}}{2})}[/tex]
Simplifying the terms, we have,
[tex]tan \ x=\frac{1}{2}\times\frac{2}{\sqrt{3}}[/tex]
[tex]tan \ x=\frac{1}{\sqrt{3}}[/tex]
Rationalizing the denominator, we get;
[tex]tan \ x=\frac{1}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}[/tex]
[tex]tan \ x=\frac{\sqrt{3}}{3}[/tex]
Thus, the value of tan x is [tex]tan \ x=\frac{\sqrt{3}}{3}[/tex]
Hence, Option B is the correct answer.
