Hello Armando,
First, subtract 1 from both sides: 2 cotx = 2
divide both sides by 2: cot x = 1
From here, you can recall that cot x = 1/tanx so you'd rewrite the equation as: 1/tanx = 1
Cross-multiply and you get: tan x = 1.
tan x is POSITIVE in quadrants 1 and 3, so that's where your answers will lie.
tan x = 1 when x = π/4 (quadrant 1 solution) or x = 5π/4 (quadrant 3 solution)
Those are the only solutions that fit into the [0,2π) interval, so your solution set is: π/4, 5π/4
