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Byju's Answer
Standard XII
Mathematics
Circular Measurement of Angle
Given that ...
Question
Given that
tan
h
x
=
sin
h
x
cos
h
x
, express the value of
tan
h
x
in terms of
e
x
and
e
−
x
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Solution
t
a
n
h
x
=
s
i
n
h
x
c
o
s
h
x
⇒
t
a
n
h
x
=
(
e
x
−
e
−
x
2
)
(
e
x
+
e
−
x
2
)
⇒
t
a
n
h
x
=
e
x
−
e
−
x
e
x
+
e
−
x
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Similar questions
Q.
There are six trigonometric and six inverse trigonometric functions. Similarly there are six hyperbolic function defined as follows:
The quantity
e
x
−
e
−
x
2
where
x
ϵ
R
is called hyperbolic sine of
x
and is written as
sinh
x
,
cosh
x
=
e
x
+
e
−
x
2
called as hyperbolic cos
x
and hyperbolic tan of
x
is written as
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x
=
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cosh
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,
cosech
x
=
1
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,
coth
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=
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x
.
Which of the following is many one ?
Q.
Assuming the derivatives of
sin
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and
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h
x
, use the quotient rule to prove that if
y
=
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x
=
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cos
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x
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d
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d
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Q.
Using
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x
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−
e
−
x
e
x
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−
x
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Q.
Given that
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h
x
=
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, find the values of
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x
Determine the value of
x
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Q.
The value of
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h
x
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h
x
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