how do you solve for x 0=cos2x - cosx?

Answer 1

2 cos ² x - cos x - 1 = 0
(2 cos x + 1)(cos x - 1) = 0
cos x = - 1 / 2 , cos x = 1
x = 120° , 240° , 0° , 360°

Answer 2

let cos2x = 2cos^2x-1. Then,

0=cos2x - cosx
0 = 2cos^2x - 1 - cosx
0 = 2cos^2x - cosx -1
factoring...
0 = (2cosx + 1)(cosx - 1)
Equating the two factors on the right side to the left side of the equation(which is 0)...we have...
0 = (2cosx + 1) and 0 =(cosx - 1)
Solving these two equations separately..

0 = 2cosx + 1, or
2cosx + 1 = 0
2cosx = -1
cosx = -1/2
x = arccosx ( -1/2)
x = 2π/3 +/- 2kπ where k is an integer

For the second equation..
0 =cosx - 1
cosx - 1 = 0
cosx = 1
x = arccos(1)
x = 0 +/- 2kπ where k is an integer...

Thus, the solutions of the equation are x = 0 +/- 2kπ where k is an integer and x = 0 +/- 2kπ where k is an integer

Answer 3

cos2x - cosx = 0
2cos^2x - 1 - cos x = 0
2cos^2x - cos x - 1 = 0
(2cosx + 1)(cos x -1) = 0
either (2cosx + 1) = 0 or (cosx - 1) = 0
2cosx + 1 = 0 cos x - 1 = 0
cos x = -0.5 cos x = 1
x = 90*, 360*
Solve the other one by pressing the calculator.

Answer 4

cos2x-cosx = 0
cos2x = 2cos^2X-1
on putting cos2x as 2cos^2x-1
2cos^2x-1-cosx = 0
let cosx = t
2t^2-t-1 = 0
this is an quadric eqution on factorization we get
(t-1)(2t+1) = 0
if t -1 = 0
t = 1
cosx = 1
cosx = cos o
x = 2npie
if 2t+1 = 0
t = -1/2
cosx = cos(2pie/3)
x = 2npie(+-)pie/3

Answer 5

if 0 = cos2x - cosx,
then cos2x = cos x
therefore x must be equal to 0
if x = 0
cos 2x = 1
cos x = 1
1 - 1= 0

Answer 6

is cos2x = cos²(x) or cos(2x) i'm assuming its cos²(x). if that is cos²(x) that's comparable to (cosx)² cos²x + cosx = 0 cosx(cosx+a million) = 0 cosx = 0 or cosx = -a million x = 90º or 180º or 270º x = ?/2 rad or ? rad or 3?/2 rad

Answer 7

0 = cos 2x - cosx

But cos 2x = 2cos(x)^2 - 1
so
0 = 2cos(x)^2 - 1 - cos(x)
= 2cos(x)^2 - cos(x) - 1
= (2cos(x) + 1)(cos(x) - 1)

cos(x) - 1 = 0 or 2cos(x) + 1 = 0

cos(x) = 1; x = 0 or 2 pi or ...

2cos(x) + 1 = 0
cos(x) = -1/2
x = 2 pi/3 or 4 pi/3 or 8 pi/3 or 10 pi/3 or ...

Answer 8

rewrite cos2x as 2cos^2x-1, then factor.

Answer 9

use your calcu. man.