2sin x + 7cos x - 3cot x + 10
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Step-by-step explanation:
The equation can be rewritten as
2
sin
x
1
−
3
cos
x
sin
x
−
3
sin
x
=
0
If we multiply both sides by
sin
x
we get
2
sin
2
x
−
3
cos
x
−
3
=
0
Using the identity:
sin
2
x
+
cos
2
x
≡
1
We can find that
sin
2
x
≡
1
−
cos
2
x
So,
2
(
1
−
cos
2
x
)
−
3
cos
x
−
3
=
0
2
−
2
cos
2
x
−
3
cos
x
−
3
=
−
2
cos
2
x
−
3
cos
x
−
1
=
0
2
cos
2
x
+
3
cos
x
+
1
=
0
By substituting
x
for
cos
we get:
2
x
2
+
3
x
+
1
=
0
x
=
−
b
±
√
b
2
−
4
a
c
2
a
x
=
−
3
+
√
3
2
−
4
(
2
⋅
1
)
2
(
2
)
=
−
1
2
x
=
−
3
−
√
3
2
−
4
(
2
⋅
1
)
2
(
2
)
=
−
1
cos
x
=
−
1
or
−
1
2
x
=
arccos
(
−
1
)
=
180
x
=
arccos
(
−
1
2
)
=
120
However,
cos
(
360
+
180
)
=
−
1
and
cos
(
360
−
120
)
=
−
1
2
x
=
n
360
±
180
,
n
360
±
120
x
=
2
n
π
±
π
,
2
n
π
±
2
π
3
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