Square root 3 × sin X ×1/square root 3 = 1× cos 2 X

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
)
.
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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
.
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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