Question

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

Answer 1

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

Explanation:

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, ...`