The trigonometric equation tan x + cot x = 1 has to be solved for x.
tan x + cot x = 1
Let tan x = y
=> y + 1/y = 1
=> y^2 + 1 = y
=> y^2 - y + 1 = 0
Here b^2 - 4ac = (-1)^2 - 4*1*1 = -3 which is negative. The equation derived has complex roots. tan x can only take on real values. As a result it is not possible to determine the value of x.
The given quadratic equation has no roots.