How to find the solutions of cot^2(x) - 1 = 0?

Question

How do you find the solutions of cot^2(x) - 1 = 0? Any help at all would be appreciated.

Answer 1

cot²(x) - 1 = 0

Add 1 to each side

cot²(x) = 1

cot(x) = ±1

 If cot(x) = 1 then x = π/4, 7π/4

if cot(x) = -1 then 3π/4 , 5π/4

The solutions of equation : π/4, 3π/4 , 5π/4 , 7π/4.

Comments

cot x = ± 1.

cot x = cot (± π/4)

The genaral solution of cot(θ) = cot(α) is θ = nπ + α, where n is an integer.

⇒ x = nπ ± π/4, where n is an integer.

The general solution of the equation is x = nπ ± π/4, where n is an integer.