How do you solve $tan^2x-2tanx+1=0$ ?

Question

8075 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-06T23:53:40

Please see the explanation for steps leading to the answer:
$x = pi/4 + npi$ where $n = ..., -3, -2, -1, 0, 1, 2, 3, ...$

Given:

$tan^2(x) - 2tan(x) + 1 = 0$

The above fits the pattern $a^2 + 2ab + b^2 = (a - b)^2$ where $a = tan(x) and b = 1$ :

$(tan(x) - 1)^2 = 0$

$tan(x) = 1$

$x = pi/4 + npi$ where $n = ..., -3, -2, -1, 0, 1, 2, 3, ...$

How do you solve tan^2x-2tanx+1=0tan^2x-2tanx+1=0?