SOLUTION: Find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) Sec^2x - secx = 2

 = .


Introduce new variable u = seq(x). Then your equation becomes

 = ,

 = .

Factor the left side. You will get

(u-2)*(u+1) = 0.

The solutions are 

u = 2  and/or  u = -1.

From this point you have two equations:

1)  sec(x) = 2  --->   = 2  --->  cos(x) =   --->  x = +/- + ,  k = 0, +/-1, +/-2, . . . and

2)  sec(x) = -1  --->   = -1  --->  cos(x) =   --->  x =  + ,  k = 0, +/-1, +/-2, . . .


Answer.  x = +/- + ,  k = 0, +/-1, +/-2, . . . and
         x = ,  k = 0, +/-1, +/-2, . . .