tan(x) = cot(x)
tan(x) = 1 / tan(x)
tan²(x) = 1
tan²(x) - 1 = 0
(tan(x) - 1) (tan(x) + 1) = 0
tan(x) - 1 = 0 or tan(x) + 1 = 0
tan(x) = 1 or tan(x) = -1
x = π/4 + nπ or x = -π/4 + nπ
where in both cases, n is any integer.
In the interval 0 < x < π, we get solutions:
• x = π/4 from the first family (when n = 0)
• x = 3π/4 from the second family (when n = 1)
So the equation has solutions x = π/4 or x = 3π/4.
