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AP EAPCET 25-Aug-2021 Shift 2 Paper
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© examsnet.com
Question : 8
Total: 160
If the determinant
|
cos
2
x
sin
2
x
cos
2
x
sin
2
x
cos
2
x
cos
2
x
cos
2
x
cos
2
x
cos
2
x
|
is expanded in powers of
cos
x
, then the constant term in the expansion is
1
-1
0
2
Validate
Solution:
👈: Video Solution
Let Δ =
|
cos
2
x
sin
2
x
cos
2
x
sin
2
x
cos
2
x
cos
2
x
cos
2
x
cos
2
x
cos
2
x
|
On expanding along
R
1
.
Δ
=
cos
2
x
[
cos
2
2
x
−
cos
4
x
]
−
sin
2
x
[
sin
2
x
cos
2
x
−
cos
2
x
.
cos
2
x
]
+
cos
2
x
[
sin
2
x
cos
2
x
−
cos
2
2
x
]
Δ
=
cos
2
x
[
(
2
cos
2
x
−
1
)
2
−
cos
4
x
]
−
sin
2
x
[
cos
2
x
(
sin
2
x
−
cos
2
x
)
]
+
cos
2
x
[
cos
2
x
−
cos
4
x
−
4
cos
4
x
−
1
+
4
cos
2
x
]
=
(
2
cos
2
x
−
1
)
[
3
cos
4
x
+
1
+
5
cos
2
x
−
5
cos
4
x
−
1
]
+
(
1
−
cos
2
x
)
[
(
2
cos
2
x
−
1
)
2
]
⇒
(
2
cos
2
x
−
1
)
[
5
cos
2
x
−
2
cos
4
x
]
+
(
2
cos
2
x
−
1
)
[
2
cos
2
x
−
1
−
2
cos
3
x
+
cos
2
x
]
⇒
(
2
cos
2
x
−
1
)
[
5
cos
2
x
−
2
cos
4
x
+
3
cos
2
x
−
2
cos
3
x
−
1
]
⇒
(
2
cos
2
x
−
1
)
[
8
cos
2
x
−
2
cos
4
x
−
2
cos
3
x
−
1
]
Hence, constant term will be
(
−
1
)
×
(
−
1
)
=
1
© examsnet.com
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