cos ^2x - 2cos X -1=0 use foil

Question

The problem is:

cos ^2x - 2cos X -1=0

 

My answer was:

(cosx + 1)(cos(-x) - 1)

 

All wrong... Please help

 

 

Answer 1

You can solve it by completing the square.

cos^2 x - 2cos x + 1 = 2

(cos x - 1)^2 = 2

cos x = 1 - sqrt(2)

In (0, 2pi), x = 1.998 rad, 2pi-1.998 rad