Posted by Josh on .
Solve Cos^2(x)+cos(x)=cos(2x). Give exact answers within the interval [0,2π)
Ive got the equation down to cos^2(x)+cos(x)+1=0 or and it can be simplified too sin^2(x)+cos(x)=0
If you could tell me where to go from either of these two, it would be great help.. Thankyou for any responses

Precalculus 
Steve,
cos^2(x) + cos(x) = 2cos^2(x)  1
cos^2(x)  cos(x)  1 = 0
This is just like
u^2  u  1 = 0
u = [1 +/ sqrt(5)]/2
since u = cos(x) and must be less than 1,
cos(x) = (1sqrt(5))/2
will be in QII or QIII