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Trigonometry Examples
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Trigonometry
Expand the Trigonometric Expression tan(2x)
tan
(
2
x
)
tan
(
2
x
)
Step 1
Apply the
tangent
double
-
angle
identity
.
2
tan
(
x
)
1
−
tan
2
(
x
)
2
tan
(
x
)
1
-
tan
2
(
x
)
Step 2
Simplify the
denominator
.
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Step 2.1
Rewrite
1
1
as
1
2
1
2
.
2
tan
(
x
)
1
2
−
tan
2
(
x
)
2
tan
(
x
)
1
2
-
tan
2
(
x
)
Step 2.2
Since both
terms
are
perfect squares
,
factor
using the
difference of squares
formula
,
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
a
2
-
b
2
=
(
a
+
b
)
(
a
-
b
)
where
a
=
1
a
=
1
and
b
=
tan
(
x
)
b
=
tan
(
x
)
.
2
tan
(
x
)
(
1
+
tan
(
x
)
)
(
1
−
tan
(
x
)
)
2
tan
(
x
)
(
1
+
tan
(
x
)
)
(
1
-
tan
(
x
)
)
2
tan
(
x
)
(
1
+
tan
(
x
)
)
(
1
−
tan
(
x
)
)
2
tan
(
x
)
(
1
+
tan
(
x
)
)
(
1
-
tan
(
x
)
)
t
a
n
(
2
x
)
t
a
n
(
2
x
)
(
(
)
)
|
|
[
[
]
]
√
√
≥
≥
°
°
7
7
8
8
9
9
≤
≤
θ
θ
4
4
5
5
6
6
/
/
^
^
×
×
>
>
π
π
1
1
2
2
3
3
-
-
+
+
÷
÷
<
<
,
,
0
0
.
.
%
%
=
=
⎡
⎢
⎣
x
2
1
2
√
π
∫
x
d
x
⎤
⎥
⎦
[
x
2
1
2
π
∫
x
d
x
]
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