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Byju's Answer
Standard XII
Mathematics
Solving Simultaneous Trigonometric Equations
If sinα+ si...
Question
If
sin
α
+
sin
β
=
a
and
cos
α
+
cos
β
=
b
, then the value of
sin
α
+
β
=
m
a
b
a
2
+
b
2
.Find
m
Open in App
Solution
sin
α
+
sin
β
=
a
,
cos
α
+
cos
β
=
b
a
2
+
b
2
=
sin
2
α
+
sin
2
β
+
cos
2
α
+
cos
2
β
+
2
(
sin
α
sin
β
+
cos
α
cos
β
)
a
2
+
b
2
=
2
+
2
cos
(
α
−
β
)
∴
1
+
cos
(
α
−
β
)
=
a
2
+
b
2
2
a
b
=
sin
α
cos
α
+
sin
α
cos
β
+
sin
β
cos
α
+
sin
β
cos
β
=
sin
(
α
+
β
)
+
sin
2
α
+
sin
2
β
2
=
sin
(
α
+
β
)
+
sin
(
α
+
β
)
cos
(
α
−
β
)
=
sin
(
α
+
β
)
[
1
+
cos
(
α
−
β
)
]
a
b
=
sin
(
α
+
β
)
(
a
2
+
b
2
2
)
∴
sin
(
α
+
β
)
=
2
a
b
a
2
+
b
2
Given,
sin
(
α
+
β
)
=
m
a
b
a
2
+
b
2
∴
m
=
2
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1
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