Solve on the interval [0, 2pi) : 3 sec x - 2 = 1

First we rewrite the expression:

3sec (x) - 2 = 1

3 (1 / cos (x)) - 2 = 1

3 (1 / cos (x)) = 1 + 2

3 (1 / cos (x)) = 3

(1 / cos (x)) = 3/3

cos (x) = 1

x = 2 * pi * n

on the interval [0, 2pi):

x = 0

Answer:

x = 0 on the interval [0, 2pi)