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Byju's Answer
Standard XII
Mathematics
Sin(A+B)Sin(A-B)
If tanβ =2s...
Question
If
tan
β
=
2
sin
α
⋅
sin
γ
⋅
c
o
s
e
c
(
α
+
γ
)
then
cot
α
,
cot
β
,
cot
γ
are in
A
A.P.
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B
G.P.
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C
H.P.
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D
none of these
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Solution
The correct option is
B
A.P.
t
a
n
β
=
2
sin
α
⋅
sin
γ
s
i
n
(
α
+
γ
)
⇒
sin
(
α
+
γ
)
2
sin
α
⋅
sin
γ
=
c
o
t
β
⇒
sin
α
⋅
cos
γ
+
cos
α
⋅
sin
γ
2
sin
α
⋅
sin
γ
=
c
o
t
β
⇒
c
o
t
γ
+
c
o
t
α
=
2
c
o
t
β
⇒
c
o
t
α
,
c
o
t
β
and
c
o
t
γ
are in A.P
Suggest Corrections
0
Similar questions
Q.
lf
tan
β
=
2
sin
α
sin
γ
cosec
(
α
+
γ
)
, then
cot
α
,
cot
β
,
cot
γ
are in
Q.
If
tan
β
=
2
sin
α
sin
γ
c
o
s
e
c
(
α
+
γ
)
, then
cot
α
,
cot
β
,
cot
γ
are in
Q.
if
α
+
β
+
γ
=
90
0
, then tan
α
+
t
a
n
β
+
t
a
n
α
t
a
n
β
c
o
t
γ
is--.
Q.
If
α
,
β
,
γ
are the roots of
a
x
3
+
b
x
2
+
c
x
+
d
=
0
and
∣
∣ ∣ ∣
∣
α
β
γ
β
γ
α
γ
α
β
∣
∣ ∣ ∣
∣
=
0
,
α
≠
β
≠
γ
, then find the equation whose roots are
α
+
β
−
γ
,
γ
+
α
−
β
,
β
+
γ
−
α
Q.
If
α
,
β
,
γ
are the roots of
x
3
+
q
x
+
r
=
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then
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−
γ
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+
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Sin(A+B)Sin(A-B)
Standard XII Mathematics
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