Question

How do you solve `\tan ( 2\theta ) = 1`?

Answer 1

`theta = n*pi/2 + pi/8`, where `n` is an integer

Explanation:

We start with `tan(2theta)=1`

So tangent of what angle equals `1`? Tangent of `pi/4` equals `1` and tangent of `(5pi)/4` equals `1` and tangent `(9pi)/4`, and by extension tangent of any `n*pi + pi/4 = 1`, where `n` is an integer

Therefore our angle `2theta= n*pi + pi/4`

So `theta = n*pi/2 + pi/8`