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Byju's Answer
Standard X
Mathematics
Standard Values of Trigonometric Ratios
If 2tan2x -...
Question
If
2
tan
2
x
−
5
sec
x
=
1
for exactly seven distinct values of
x
ϵ
[
0
,
n
π
2
]
,
n
ϵ
N
, then find the greatest value of
n
.
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Solution
Given,
2
tan
2
x
−
5
sec
x
=
1
2
(
sec
2
x
−
1
)
−
5
sec
x
=
1
2
sec
2
x
−
2
−
5
sec
x
=
1
2
sec
2
x
−
5
sec
x
−
3
=
0
2
sec
x
(
sec
x
−
3
)
+
1
(
sec
x
−
3
)
=
0
(
2
sec
x
+
1
)
(
sec
x
−
3
)
=
0
sec
x
=
−
1
2
,
sec
x
=
3
=
6
π
+
π
2
=
13
π
2
n
π
2
=
13
π
2
∴
n
=
13
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2
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