Cos2x cosx 0
Asked by maham237 @ in Mathematics viewed by 300 People
Solve the equation
cos2x−cosx=0
on the interval [0,2π)
Answered by maham237 @
cos 2x – cosx = 0
------------ (1)
where cos2x = 2cos^2x –
1
equation (1) becomes;
2cos^2x – 1 – cosx = 0 ------------ (2)
Suppose cosx = y, then
equation (2) becomes;
2y^2 – 1 – y = 0
By factorization method;
(2y + 1) x (y – 1) = 0
Where 2y + 1 = 0 or y –
1 = 0
So solving both;
y = -1/2 or 1
As y = cosx
So cosx = -1/2 or 1
The above equation is true only for x = 2/3π, 0, 4/3 π
The solution were find out for interval [0,2 π),
where 2 π is not included in the interval, as the interval is not a closed on
the right side.
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