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EAMCET Engineering 2005 Solved Paper
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© examsnet.com
Question : 108
Total: 160
If
cos
2
x
=
(
√
2
+
1
)
(
cos
x
−
1
√
2
)
,
cos
x
≠
1
2
then
x
∈
{
2
n
π
±
π
3
:
n
∈
Z
}
{
2
n
π
±
π
6
:
n
∈
Z
}
{
2
n
π
±
π
2
:
n
∈
Z
}
{
2
n
π
±
π
4
:
n
∈
Z
}
Validate
Solution:
cos
2
x
=
(
√
2
+
1
)
(
cos
x
−
1
√
2
)
⇒
cos
2
x
=
√
2
cos
x
−
1
+
cos
x
−
1
√
2
⇒
1
+
cos
2
x
=
cos
x
(
√
2
+
1
)
−
1
√
2
⇒
2
cos
2
x
−
cos
x
(
√
2
+
1
)
+
1
√
2
=
0
⇒
cos
x
=
(
√
2
+
1
)
±
√
(
√
2
+
1
)
2
−
8
√
2
2
(
2
)
=
(
√
2
+
1
)
±
√
3
+
2
√
2
−
4
√
2
4
=
(
√
2
+
1
)
±
√
(
√
2
−
1
)
2
4
=
√
2
+
1
±
(
√
2
−
1
)
4
on taking + ve sign
cos
x
=
√
2
+
1
+
√
2
−
1
4
=
2
√
2
4
=
1
√
2
⇒
x
=
2
n
π
±
π
4
∀
n
∈
Z
© examsnet.com
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