Justify the small angle approximation for tangent

Assume that angle x is small, using small angle approximation,

$\mathrm{sin}(x)=x$

$\mathrm{cos}(x)=1-\frac{{x}^{2}}{2}$;

and $\mathrm{tan}(x)=x$.

I am able to justify the first two using Maclaurin's Theorem but not the last one. How do we justify the last one?

Assume that angle x is small, using small angle approximation,

$\mathrm{sin}(x)=x$

$\mathrm{cos}(x)=1-\frac{{x}^{2}}{2}$;

and $\mathrm{tan}(x)=x$.

I am able to justify the first two using Maclaurin's Theorem but not the last one. How do we justify the last one?