Answer:
Step-by-step explanation:
To solve the equation
2
cos
(
�
)
−
1
=
0
2
cos(x)−1=0, we can isolate
cos
(
�
)
cos(x) and then solve for
�
x:
2
cos
(
�
)
−
1
=
0
2
cos(x)−1=0
Add 1 to both sides:
2
cos
(
�
)
=
1
2
cos(x)=1
Divide both sides by
2
2
:
cos
(
�
)
=
1
2
cos(x)=
2
1
Now, we need to find all values of
�
x between
0
0 and
2
�
2π where
cos
(
�
)
cos(x) equals
1
2
2
1
.
In the interval
0
≤
�
≤
2
�
0≤x≤2π,
cos
(
�
)
cos(x) equals
1
2
2
1
at the following angles:
�
=
�
4
,
7
�
4
x=
4
π
,
4
7π
So, the exact solutions of
2
cos
(
�
)
−
1
=
0
2
cos(x)−1=0 for
0
≤
�
≤
2
�
0≤x≤2π in radians are
�
=
�
4
x=
4
π
and
�
=
7
�
4
x=
4
7π
.
