MATH SOLVE

7 months ago

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

Accepted Solution

A:

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