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Byju's Answer
Standard XII
Mathematics
Solving Simultaneous Trigonometric Equations
If sin α+si...
Question
If
s
i
n
α
+
s
i
n
β
=
a
and
c
o
s
α
+
c
o
s
β
=
b
then show that,
sin
(
α
+
β
)
=
2
a
b
a
2
+
b
2
.
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Solution
sin
(
α
+
β
)
=
2
a
b
a
2
+
b
2
a
=
sin
α
+
sin
β
=
2
sin
(
α
+
β
2
)
.
cos
(
α
−
β
2
)
b
=
cos
α
+
cos
β
=
2
cos
(
α
+
β
2
)
.
cos
(
α
−
β
2
)
a
b
=
4
sin
(
α
+
β
2
)
.
cos
(
α
+
β
2
)
.
cos
(
α
−
β
2
)
=
2
sin
(
α
+
β
)
.
cos
2
(
α
−
β
2
)
a
2
+
b
2
=
4
cos
2
(
α
−
β
2
)
∴
2
a
b
a
2
+
b
2
=
sin
(
α
+
β
)
p
r
o
v
e
d
.
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0
Similar questions
Q.
If
s
i
n
α
+
s
i
n
β
=
a
a
n
d
c
o
s
α
+
c
o
s
β
=
b
, prove that
(i)
s
i
n
(
α
+
β
)
=
2
a
b
a
2
+
b
2
(ii)
c
o
s
(
α
−
β
)
=
a
2
+
b
2
−
2
2
Q.
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
Q.
If
sin
α
+
sin
β
=
a
and
cos
α
+
cos
β
=
b
, prove that
tan
α
−
β
2
=
±
√
x
−
a
2
−
b
2
a
2
+
b
2
. Find
x
Q.
If
sin
α
+
sin
β
=
a
and
cos
α
+
cos
β
=
b
, then the value of
sin
(
α
+
β
)
is equal to
Q.
If
cos
α
cos
β
=
a
,
sin
α
sin
β
=
b
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)
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1
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