Answer:
The solutions are
S
=
{
1
2
π
,
3
2
π
,
1
6
π
,
5
6
π
}
Explanation:
We need
sin
2
x
=
2
sin
x
cos
x
Therefore,
sin
2
x
=
cos
x
sin
2
x
−
cos
x
=
0
2
sin
x
cos
x
−
cos
x
=
0
cos
x
(
2
sin
x
−
1
)
=
0
So,
{
cos
x
=
0
2
sin
x
−
1
=
0
⇔
,
{
cos
x
=
0
sin
x
=
1
2
⇔
,
{
x
=
π
2
3
2
π
x
=
1
6
π
5
6
π
∀
x
∈
[
0
,
2
π
]
The solutions are
S
=
{
1
2
π
,
3
2
π
,
1
6
π
,
5
6
π
}
graph{sin(2x)-cosx [-1.622, 9.475, -2.51, 3.04]}