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Byju's Answer
Standard XII
Mathematics
Product of Trigonometric Ratios in Terms of Their Sum
If α ,β ,γ∈...
Question
If
α
,
β
,
γ
∈
[
0
,
π
2
]
, then the value of
sin
(
α
+
β
+
γ
)
sin
α
sin
β
+
sin
γ
is
A
1
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B
−
1
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C
0
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D
None of these
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Solution
The correct option is
B
None of these
The value of
sin
(
α
+
β
+
γ
)
is
=
sin
α
+
sin
β
+
sin
γ
−
sin
α
cos
β
cos
γ
−
cos
α
sin
β
cos
γ
−
cos
α
cos
β
sin
γ
+
sin
α
sin
β
cos
γ
Therefore,
sin
α
+
sin
β
+
sin
γ
>
sin
(
α
+
β
+
γ
)
⇒
sin
(
α
+
β
+
γ
)
sin
α
+
sin
β
+
sin
γ
<
1
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0
Similar questions
Q.
If
α
,
β
,
γ
∈
(
0
,
π
2
)
then the value of
sin
(
α
+
β
+
γ
)
sin
α
+
sin
β
+
sin
γ
is
Q.
If
0
<
α
,
β
,
γ
<
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/
2
, prove that
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+
sin
β
+
sin
γ
>
sin
(
α
+
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+
γ
)
Q.
Prove that: If
0
<
α
,
β
,
γ
<
π
2
, prove that
sin
α
+
sin
β
+
sin
γ
>
sin
(
α
+
β
+
γ
)
.
Q.
If
α
,
β
,
γ
ϵ
(
0
,
π
2
)
, then
sin
(
α
+
β
+
γ
)
sin
α
+
sin
β
+
sin
γ
is-
Q.
If
cos
α
+
cos
β
+
cos
γ
=
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=
sin
α
+
sin
β
+
sin
γ
=
0
then
cos
(
2
α
−
β
−
γ
)
+
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β
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α
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Product of Trigonometric Ratios in Terms of Their Sum
Standard XII Mathematics
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