TITLE: Help with solving trig identity problem
QUESTION [5 upvotes]: It's been 20 years since I did trig, and this one seems a little tricky. How would I solve 
$$
\tan^2(x) -2\tan(x)=1
$$
with steps?

REPLY [4 votes]: Put $\tan x = z$
Then equation becomes,
$z^2 - 2z = 1$
$z^2 - 2z - 1 = 0$
Hope you can now factorise.