cos
(
2
x
)
β
β
3
sin
(
x
)
=
1
cos
(
2
x
)
-
3
sin
(
x
)
=
1
Factor
sin
(
x
)
sin
(
x
)
out of
β
2
sin
2
(
x
)
β
β
3
sin
(
x
)
-
2
sin
2
(
x
)
-
3
sin
(
x
)
.
Tap for more steps...
sin
(
x
)
(
β
2
sin
(
x
)
β
β
3
)
=
0
sin
(
x
)
(
-
2
sin
(
x
)
-
3
)
=
0
If any individual factor on the left side of the equation is equal to
0
0
, the entire expression will be equal to
0
0
.
sin
(
x
)
=
0
sin
(
x
)
=
0
β
2
sin
(
x
)
β
β
3
=
0
-
2
sin
(
x
)
-
3
=
0
Set
sin
(
x
)
sin
(
x
)
equal to
0
0
and solve for
x
x
.
Tap for more steps...
x
=
2
Ο
n
,
Ο
+
2
Ο
n
x
=
2
Ο
n
,
Ο
+
2
Ο
n
, for any integer
n
n
Set
β
2
sin
(
x
)
β
β
3
-
2
sin
(
x
)
-
3
equal to
0
0
and solve for
x
x
.
Tap for more steps...
x
=
4
Ο
3
+
2
Ο
n
,
5
Ο
3
+
2
Ο
n
x
=
4
Ο
3
+
2
Ο
n
,
5
Ο
3
+
2
Ο
n
, for any integer
n
n
The final solution is all the values that make
sin
(
x
)
(
β
2
sin
(
x
)
β
β
3
)
=
0
sin
(
x
)
(
-
2
sin
(
x
)
-
3
)
=
0
true.
x
=
2
Ο
n
,
Ο
+
2
Ο
n
,
4
Ο
3
+
2
Ο
n
,
5
Ο
3
+
2
Ο
n
x
=
2
Ο
n
,
Ο
+
2
Ο
n
,
4
Ο
3
+
2
Ο
n
,
5
Ο
3
+
2
Ο
n
, for any integer
n
n
Consolidate
2
Ο
n
2
Ο
n
and
Ο
+
2
Ο
n
Ο
+
2
Ο
n
to
Ο
n
Ο
n
.
x
=
Ο
n
,
4
Ο
3
+
2
Ο
n
,
5
Ο
3
+
2
Ο
n
x
=
Ο
n
,
4
Ο
3
+
2
Ο
n
,
5
Ο
3
+
2
Ο
n
, for any integer
n