Question

cos2x=secx find x

Answer 1

cos2x = secx
2cos^2(x)-1 = 1/cosx
2cos^3(x) - cosx - 1 = 0
you will probably need to use a graphical or numeric method to solve this.

However, you know that cos2x never gets more than 1, and secx never gets less than 1.

So, you will need
cos2x = secx = 1
or
cos2x = secx = -1

Try that on for size