Question

Solve sec to the power of 2 times x minus 1 = 3, x such that [0,2pi).

Answer 1

By "sec" do you mean 2?

Answer 2

if you mean

sec^2 x - 1 = 3
then we can proceed to

sec^2 x = 4
sec x = 2 or -2

sec pi/3 = 2, so using that as a reference angle in each quadrant,

x = pi/3 or 2pi/3 or 4pi/3 or 5pi/3