Explanation:
3 sec(x) - 1 = 2
Adding 1 to both sides:
3 sec(x) = 3
Dividing by 3:
sec(x) = 1
Taking the inverse secant of both sides:
x = cos^-1(1)
Since cosine has a period of 2π, the solutions to this equation occur at:
x = 0 + 2πn and x = 2π - 2πn, where n is an integer.
Substituting in n = 0, we get:
x = cos^-1(1) = 0
Substituting in n = 1, we get:
x = 2π - cos^-1(1) = 2π
Therefore, the solutions on the interval [0, 2π] are:
x = 0 and x = 2π.