Question
find all solutions to the equation in the interval [0,2pie]
cos2x=cosx
cos2x=cosx
Answers
MathMate
See:
http://www.jiskha.com/display.cgi?id=1303866873
http://www.jiskha.com/display.cgi?id=1303866873
Reiny
cos 2x = cosx
2cos^2 x - 1 - cosx = 0
(2cosx + 1)(cosx -1) = 0
cosx = -1/2 or cosx = 1
if cosx = -1/2, x is in II or III
x = 2π/3 or 4π/3 ......I knew cos π/3 = +1/2
if cosx = 1, then x = 0 or x = 2π
2cos^2 x - 1 - cosx = 0
(2cosx + 1)(cosx -1) = 0
cosx = -1/2 or cosx = 1
if cosx = -1/2, x is in II or III
x = 2π/3 or 4π/3 ......I knew cos π/3 = +1/2
if cosx = 1, then x = 0 or x = 2π