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Byju's Answer
Standard XII
Mathematics
Standard Limits to Remove Indeterminate Form
limx→ 0xtan 2...
Question
lim
x
→
0
x
tan
2
x
−
2
x
tan
x
(
1
−
cos
2
x
)
2
equals :
A
1
2
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B
1
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C
−
1
2
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D
1
4
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Solution
The correct option is
A
1
2
lim
x
→
0
x
tan
2
x
−
2
x
tan
x
(
1
−
cos
2
x
)
2
=
lim
x
→
0
x
2
tan
x
1
−
tan
2
x
−
2
x
tan
x
(
2
sin
2
x
)
2
=
lim
x
→
0
2
x
tan
x
tan
2
x
1
−
tan
2
x
4
sin
4
x
=
lim
x
→
0
x
tan
2
x
tan
2
x
4
sin
4
x
=
lim
x
→
0
(
tan
x
x
)
2
⋅
(
tan
2
x
2
x
)
2.
(
sin
x
x
)
4
=
1
2
Suggest Corrections
0
Similar questions
Q.
(a) Prove that
sin
[
t
a
n
−
1
1
−
x
2
2
x
+
cos
−
1
1
−
x
2
1
+
x
2
]
=
1
.
(b) If
sin
−
1
(
x
−
x
2
2
+
x
3
4
−
.
.
.
.
.
)
+
cos
−
1
(
x
2
−
x
4
2
+
x
6
4
−
.
.
.
.
.
.
.
)
=
π
2
for
0
<
|
x
|
<
√
2
, then x equals
Q.
Solve:
∫
2
x
tan
−
1
x
2
(
1
+
x
4
)
d
x
Q.
If
−
1
≤
x
≤
0
, then
sin
{
tan
−
1
1
−
x
2
2
x
−
cos
−
1
1
−
x
2
1
+
x
2
}
is equal to
Q.
If
0
≤
x
≤
1
, then
sin
{
tan
−
1
1
−
x
2
2
x
+
cos
−
1
1
−
x
2
1
+
x
2
}
is equal to
Q.
If
0
≤
x
<
1
, then
sin
{
tan
−
1
1
−
x
2
2
x
+
cos
−
1
1
−
x
2
1
+
x
2
}
is equal to
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