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Byju's Answer
Standard XI
Mathematics
Sin(A+B)Sin(A-B)
If α, β, Y ar...
Question
If
α
,
β
,
γ
are in A.P., then
sin
α
−
sin
γ
cos
γ
−
cos
α
is equal to
A
cot
β
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B
−
tan
β
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C
−
cot
β
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D
tan
β
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Solution
The correct option is
A
cot
β
sin
α
−
sin
γ
cos
γ
−
cos
α
=
sin
α
−
sin
γ
−
(
cos
α
−
cos
γ
)
=
2
cos
(
α
+
γ
2
)
sin
(
α
−
γ
2
)
2
sin
(
α
+
γ
2
)
sin
(
α
−
γ
2
)
=
cot
(
α
+
γ
2
)
=
cot
β
(
∵
2
β
=
α
+
γ
)
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0
Similar questions
Q.
If
α
,
β
,
γ
are in A.P., then
sin
α
−
sin
γ
cos
γ
−
cos
α
is equal to
Q.
If
α
,
β
,
γ
are in A.P. show that
cot
β
=
sin
α
−
sin
γ
cos
γ
−
c
o
s
α
.
Q.
If
sin
α
+
sin
β
+
sin
γ
=
0
and
cos
α
+
cos
β
+
cos
γ
=
0
, then value of
cos
(
α
−
β
)
+
cos
(
β
−
γ
)
+
cos
(
γ
+
α
)
is
Q.
If
c
o
s
α
+
c
o
s
β
+
c
o
s
γ
=
s
i
n
α
+
s
i
n
β
+
s
i
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γ
=
0
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β
+
γ
)
+
c
o
s
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γ
+
α
)
+
c
o
s
(
α
+
β
)
=
0
s
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(
β
+
γ
)
s
i
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γ
+
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)
+
s
i
n
(
α
+
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Q.
If
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,
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are inAP. show that
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Sin(A+B)Sin(A-B)
Standard XI Mathematics
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