cos
(
2
x
)
−
√
3
sin
(
x
)
=
1
cos
(
2
x
)
-
3
sin
(
x
)
=
1
Factor 
sin
(
x
)
sin
(
x
)
 out of 
−
2
sin
2
(
x
)
−
√
3
sin
(
x
)
-
2
sin
2
(
x
)
-
3
sin
(
x
)
.
Tap for more steps...
sin
(
x
)
(
−
2
sin
(
x
)
−
√
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
−
2
sin
(
x
)
−
√
3
=
0
-
2
sin
(
x
)
-
3
=
0
Set 
sin
(
x
)
sin
(
x
)
 equal to 
0
0
 and solve for 
x
x
.
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x
=
2
π
n
,
π
+
2
π
n
x
=
2
π
n
,
π
+
2
π
n
, for any integer 
n
n
Set 
−
2
sin
(
x
)
−
√
3
-
2
sin
(
x
)
-
3
 equal to 
0
0
 and solve for 
x
x
.
Tap for more steps...
x
=
4
π
3
+
2
π
n
,
5
π
3
+
2
π
n
x
=
4
π
3
+
2
π
n
,
5
π
3
+
2
π
n
, for any integer 
n
n
The final solution is all the values that make 
sin
(
x
)
(
−
2
sin
(
x
)
−
√
3
)
=
0
sin
(
x
)
(
-
2
sin
(
x
)
-
3
)
=
0
 true.
x
=
2
π
n
,
π
+
2
π
n
,
4
π
3
+
2
π
n
,
5
π
3
+
2
π
n
x
=
2
π
n
,
π
+
2
π
n
,
4
π
3
+
2
π
n
,
5
π
3
+
2
π
n
, for any integer 
n
n
Consolidate 
2
π
n
2
π
n
 and 
π
+
2
π
n
π
+
2
π
n
 to 
π
n
π
n
.
x
=
π
n
,
4
π
3
+
2
π
n
,
5
π
3
+
2
π
n
x
=
π
n
,
4
π
3
+
2
π
n
,
5
π
3
+
2
π
n
, for any integer 
n