this is as far as i have gotten:

2cotx + sec^2x = 0

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

and thats it. can someone please help me with the solution and explain each step?

### 1 Answer

Elementary, I assure you…

2cotx + sec^2x = 0

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

Now multiply through by tanx:

tan^3x + tanx + 2 = 0

By inspection, tanx = -1 is a root, in fact the only one, as synthetic division would confirm.

But if tanx = -1, then x = (4n+3)π/4, so for example 3π/4, 7π/4 etc.

Caio!