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Byju's Answer
Standard XII
Mathematics
Derivative of Standard Functions
Prove that ...
Question
Prove that
sec
2
(
tan
−
1
2
)
+
cosec
2
(
cot
−
1
3
)
=
15
.
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Solution
We know,
tan
−
1
x
=
sec
−
1
(
√
x
2
+
1
)
and
cot
−
1
x
=
cosec
−
1
(
√
x
2
+
1
)
So,
sec
2
(
tan
−
1
2
)
+
cosec
2
(
cot
−
1
3
)
=
sec
2
(
sec
−
1
√
5
)
+
cosec
2
(
cosec
−
1
√
10
)
=
(
sec
(
sec
−
1
√
5
)
)
2
+
(
cosec
(
cosec
−
1
√
10
)
)
2
=
5
+
10
(since both
√
5
and
√
10
are greater than
1
)
=
15
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Q.
s
e
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(
2
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)
+
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Q.
The value of
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Q.
The value of
sec
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cot
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Q.
Evaluate:
sec
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(
tan
−
1
2
)
+
c
o
s
e
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2
(
cot
−
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3
)
Q.
Prove that
sec
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(
tan
−
1
2
)
+
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2
(
cot
−
1
3
)
=
15
.
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Derivative of Standard Functions
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