Question

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

Answer 1

`x=npi-pi/4`, where `n` is an integer.

Explanation:

`tan^2x+2tanx+1=0`

`hArr(tanx+1)^2=0`

Hence `tanx=-1=tan(-pi/4)` and as the function tangent has a cycle of `pi`,

`x=npi-pi/4`, where `n` is an integer.