Question 544641: Find the exact solutions in the interval [ 0 , 2π] for cos 2x – cos x = 0.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find the exact solutions in the interval [ 0 , 2π] for cos 2x – cos x = 0
**
cos2x – cosx = 0
Identity: cos 2x=2cos^2x-1
2cos^2x-1 – cosx = 0
2cos^2x– cosx-1 = 0
(2cosx+1)(cosx-1)=0
..
2cosx+1=0
cosx=-1/2
x=2π/3 and 4π/3 (in quadrants II and III where cos<0
..
cosx-1=0
cosx=1
x=0
..
ans:
Exact solutions in the interval [ 0 , 2π]
x=0, 2π/3 and 4π/3
|
|
|
