Question

Solve: sec^2x-secx=2

Answer 1

First, multiply the entire equation by cos^2 (x). This gives 1 - cos(x) = 2cos^2 (x). Then, let u = cos (x) so we have 2u^2 = 1-u. This gives u = -1 & u = 1/2. Now, we put these solutions in terms of x by letting cos (x) = -1 and cos (x) = 1/2.

For x in [0, 2 pi):

cos(x) = -1 ==> x = pi.
cos(x) = 1/2 ==> x = pi /3 and x = 5 pi /3.

So x = {pi/3, pi, and 5 pi/3} are the three solutions to this equation in [0, 2 pi).