Question

Solve tan x =cot x for 0 < x < pi

Answer 1

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.