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Byju's Answer
Standard XII
Mathematics
Sin(A+B)Sin(A-B)
sin h x =34, ...
Question
sin
h
x
=
3
4
,
find
cos
h
(
2
x
)
and
sin
h
(
2
x
)
?
Open in App
Solution
∵
sinh
x
=
3
4
w
h
e
r
e
,
p
=
3
a
n
d
h
=
4
∴
b
=
√
4
2
−
3
2
=
√
7
h
e
n
c
e
,
cosh
x
=
b
h
=
√
7
4
∴
cosh
(
2
x
)
=
1
−
2
sinh
2
x
=
1
−
2
(
3
4
)
2
=
−
1
8
a
n
d
sinh
(
2
x
)
=
2
sinh
x
.
cosh
x
=
2.
3
4
.
√
7
4
=
3
√
7
8
Suggest Corrections
2
Similar questions
Q.
Prove the following :
(a)
cosh
2
x
−
sinh
2
x
=
1
(b)
sinh
2
x
=
2
sinh
x
cosh
x
(c)
cosh
2
x
=
cosh
2
x
+
sinh
2
x
(d)
tanh
2
x
=
1
−
sech
2
x
Q.
Find the possible values of
sin
h
x
for which
12
cos
h
2
x
+
7
sin
h
x
=
24
(You may find the identity
cos
h
2
x
−
sin
h
2
x
=
1
useful)
Hence find the possible values of
x
, leaving your answers as natural logarithms
Q.
Assertion :The nature of graph of the functions
f
(
x
)
=
sinh
2
(
x
)
and
g
(
x
)
=
cosh
2
(
x
)
is same. Reason: The two functions are related by the relation
1
+
sinh
2
(
x
)
=
cosh
2
(
x
)
.
Q.
Use the definitions of
sin
h
x
and
cos
h
x
in terms of exponential functions to prove that
cos
h
2
x
=
cos
h
2
x
−
1
Q.
Show that
cos
h
x
+
sin
h
x
=
e
x
and simplify
cos
h
x
−
sin
h
x
By considering
(
cos
h
x
+
sin
h
x
)
2
−
(
cos
h
x
−
sin
h
x
)
2
show that
2
sin
h
x
cos
h
x
=
sin
h
2
x
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Sin(A+B)Sin(A-B)
Standard XII Mathematics
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