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AP EAPCET 23-Aug-2021 Shift 2 Paper
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Section:
Mathematics
© examsiri.com
Question :
24 of 160
Marks:
+1
,
-0
If
sec
−
1
x
a
−
sec
−
1
x
b
=
sec
−
1
b
sec
−
1
a
, then
x
=
a
b
−
a
b
a
2
b
2
Validate
Solution:
sec
−
1
(
x
a
)
−
sec
−
1
(
x
b
)
=
sec
−
1
b
−
sec
−
1
a
⇒
cos
−
1
(
a
x
)
−
cos
−
1
(
b
x
)
=
cos
−
1
(
1
b
)
−
cos
−
1
(
1
a
)
⇒
cos
−
1
{
a
b
x
2
+
√
1
−
a
2
x
2
.
√
1
−
b
2
x
2
}
=
cos
−
1
{
1
a
b
+
√
1
−
1
b
2
√
1
−
1
a
2
}
[
∵
cos
−
1
x
−
cos
−
1
y
=
cos
−
1
{
x
y
+
√
1
−
x
2
√
1
−
y
2
}
]
⇒
a
b
x
2
+
√
(
x
2
−
a
2
)
(
x
2
−
b
2
)
x
2
=
1
a
b
+
√
(
b
2
−
1
)
(
a
2
−
1
)
a
b
⇒
a
2
b
2
+
a
b
√
(
x
2
−
a
2
)
(
x
2
−
b
2
)
=
x
2
+
x
2
√
(
a
2
−
1
)
(
b
2
−
1
)
⇒
a
b
√
(
x
2
−
a
2
)
(
x
2
−
b
2
)
−
x
2
√
(
a
2
−
1
)
(
b
2
−
1
)
=
x
2
−
a
2
b
2
in RHS
x
2
−
a
2
b
2
has the minimum value zero because
x
2
is always positive and
a
2
b
2
is positive.
If
x
2
−
a
2
b
2
=
0
⇒
x
2
=
a
2
b
2
⇒
x
=
a
b
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