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Tardigrade
Question
Mathematics
Let α and β be nonzero real numbers such that 2( cos β- cos α)+ cos α cos β=1. Then which of the following is/are true?
Q. Let
α
and
β
be nonzero real numbers such that
2
(
cos
β
−
cos
α
)
+
cos
α
cos
β
=
1
. Then which of the following is/are true?
4202
217
JEE Advanced
JEE Advanced 2017
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A
tan
(
2
α
)
+
3
tan
(
2
β
)
=
0
B
3
tan
(
2
α
)
+
tan
(
2
β
)
=
0
C
tan
(
2
α
)
−
3
tan
(
2
β
)
=
0
D
3
tan
(
2
α
)
−
tan
(
2
β
)
=
0
Solution:
cos
β
(
2
+
cos
α
)
=
1
+
2
cos
α
1
c
o
s
β
=
2
+
c
o
s
α
1
+
2
c
o
s
α
c
o
s
β
−
1
c
o
s
β
+
1
=
c
o
s
α
−
1
3
(
c
o
s
α
+
1
)
−
2
s
i
n
2
2
β
2
c
o
s
2
2
β
=
−
2
s
i
n
2
2
α
3
×
2
c
o
s
2
2
α
tan
2
2
α
=
3
tan
2
2
β
⇒
tan
2
α
=
±
3
tan
2
β