Find all solutions of the equation in the interval 0 2 algeb

Find all solutions of the equation in the interval [0, 2) algebraically. Use the table feature of a graphing utility to check your answers numerically. (Write your answers in terms of . Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.)

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Solution

tan²x - 1 = 0

(tan x + 1)*(tan x - 1) = 0

(tan x + 1) = 0 =====> tan x = -1 ======> x = 3/4, 7/4

(tan x - 1) = 0 =====> tan x = 1 =====> x = /4, 5/4