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Byju's Answer
Standard XII
Mathematics
Sin(A+B)Sin(A-B)
If α + β - ...
Question
If
α
+
β
−
γ
=
π
, and
sin
2
α
+
sin
2
β
−
sin
2
γ
=
λ
sin
α
sin
β
cos
γ
, then write the value of
λ
.
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Solution
Identity
sin
2
A
−
sin
2
B
=
sin
(
A
+
B
)
sin
(
A
−
B
)
=
(
sin
(
A
)
+
sin
(
B
)
)
(
sin
(
A
)
−
sin
(
B
)
)
=
2
sin
(
A
+
B
2
)
cos
(
A
−
B
2
)
.2
cos
(
A
+
B
2
)
sin
(
A
+
B
2
)
=
2
sin
(
A
+
B
2
)
cos
(
A
+
B
2
)
.2
sin
(
A
−
B
2
)
cos
(
A
−
B
2
)
=
sin
(
A
+
B
)
sin
(
A
−
B
)
Given equation
sin
2
α
+
[
sin
2
β
−
sin
2
γ
]
=
sin
2
α
+
sin
(
β
−
γ
)
sin
(
β
+
γ
)
=
sin
2
α
+
sin
(
π
−
α
)
sin
(
β
+
γ
)
=
sin
2
α
+
sin
α
sin
(
β
+
γ
)
=
sin
α
[
sin
α
+
sin
(
β
+
γ
)
]
=
sin
α
[
sin
(
π
−
(
β
−
γ
)
)
+
sin
(
β
+
γ
)
]
=
sin
α
[
sin
(
β
−
γ
)
+
sin
(
β
+
γ
)
]
=
sin
α
[
2
sin
β
cos
γ
]
=
2
sin
α
sin
β
cos
γ
∴
λ
=
2
Suggest Corrections
0
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Standard XII Mathematics
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