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Byju's Answer
Standard XIII
Mathematics
General Solution of Trigonometric Equation
If α, β are t...
Question
If
α
,
β
are the roots of the equation
tan
x
+
sec
x
=
2
cos
x
where
x
∈
[
0
,
2
π
)
, then the value of
|
α
−
β
|
is
A
2
π
3
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B
5
π
6
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C
2
π
5
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D
π
2
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Solution
The correct option is
A
2
π
3
tan
x
+
sec
x
=
2
cos
x
⇒
sin
x
+
1
=
2
cos
2
x
,
x
≠
(
2
n
+
1
)
π
2
⇒
2
sin
2
x
+
sin
x
−
1
=
0
⇒
(
2
sin
x
−
1
)
(
sin
x
+
1
)
=
0
⇒
sin
x
=
1
2
,
sin
x
=
−
1
sin
x
=
−
1
not possible as
x
≠
(
2
n
+
1
)
π
2
∴
sin
x
=
1
2
⇒
x
=
π
6
,
5
π
6
∴
|
α
−
β
|
=
2
π
3
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