0. So, 2 x =\ln \frac{4}{3} \Rightarrow x =\frac{1}{2} \ln \frac{4}{3}" >
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AP EAPCET 05-Jul-2022 Shift 1 Paper
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Section:
Mathematics
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© examsnet.com
Question : 25
Total: 160
If
2
‌
cosh
‌
2
‌
x
+
10
‌
sinh
‌
2
‌
x
=
5
, then
x
=
‌
1
2
‌
log
‌
4
3
‌
1
2
‌
log
‌
2
3
‌
1
2
‌
log
‌
3
2
‌
1
2
‌
log
‌
3
4
Validate
Solution:
👈: Video Solution
Here,
2
‌
cosh
‌
2
‌
x
+
10
s
i
n
h
2
x
=
5
We know that,
‌
cosh
‌
2
‌
x
=
‌
1
2
(
e
2
x
+
e
−
2
x
)
‌
s
i
n
h
2
x
=
‌
1
2
(
e
2
x
−
e
−
2
x
)
So,
2
[
‌
1
2
(
e
2
x
+
e
−
2
x
)
]
+
10
[
‌
1
2
(
e
2
x
−
e
−
2
x
)
]
=
5
‌
⇒
e
2
x
+
e
−
2
x
+
5
e
2
x
−
5
e
−
2
x
=
5
‌
⇒
6
e
2
x
−
5
−
4
e
−
2
x
=
0
⇒
(
3
e
2
x
−
4
)
(
2
e
2
x
+
1
)
=
0
‌
‌
‌
e
2
x
=
‌
4
3
or
"
‌
e
2
x
=
−
‌
1
2
The only real solution occurs when
e
2
x
>
0
.
So,
2
x
‌
=
ln
‌
4
3
⇒
‌
‌
x
‌
=
‌
1
2
‌
ln
‌
4
3
© examsnet.com
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