Find all solutions of the equation in the interval [0, 2𝜋) algebraically. tan2(x) − 1 = 0

Answer 1

Hello Emily,

I assume you meant: tan²(x) - 1 = 0

You can add 1 to both sides: tan²(x) = 1

Square root both sides: tan (x) = ± 1 so tan (x) = 1 OR tan (x) = -1

tan x = 1 when x = π/4 or x = 5π/4

tan x = -1 when x = 3π/4 or x = 7π/4

All 4 are in the [0, 2π) interval so they are your 4 solutions to the original equation.

Solution set = { π/4, 3π/4, 5π/4, 7π/4}