If cos^2(a)=1/4, what is the value of tan(a)

$$ \tan\:a\:=\:\frac{\sin\:a}{\cos\:a} $$ $$ \tan^2a\:=\:\frac{\sin^2a}{\cos^2a} $$ $$ \sin ce\:\sin^2a=1-\cos^2a $$ $$ \tan^2a\:=\:\frac{\left(1-\cos^2a\right)}{\cos^2a} $$ $$ \tan^2a\:=\:\frac{\left(1-\frac{1}{4}\right)}{\frac{1}{4}} $$ $$ \tan^2a=\frac{3}{4}\frac{.4}{1} $$ $$ \tan^2a\:=\:3 $$ $$ \tan\:a\:=\:\sqrt{3} $$