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Byju's Answer
Standard XII
Mathematics
Sine Rule
Prove that : ...
Question
Prove that :
c
o
s
A
1
−
s
i
n
A
+
s
i
n
A
1
−
c
o
s
A
+
1
=
s
i
n
A
c
o
s
A
(
1
−
s
i
n
A
)
(
1
−
c
o
s
A
)
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Solution
we have
⇒
L
H
S
=
c
o
s
A
1
−
s
i
n
A
+
s
i
n
A
1
−
c
o
s
A
+
1
⇒
L
H
S
=
c
o
s
A
(
1
−
c
o
s
A
)
+
s
i
n
A
(
1
−
c
o
s
A
)
+
(
1
−
s
i
n
A
)
(
1
+
c
o
s
A
)
s
i
n
A
(
1
−
c
o
s
A
)
+
(
1
−
s
i
n
A
)
(
1
+
c
o
s
A
)
⇒
L
H
S
=
c
o
s
A
−
c
o
s
2
A
+
s
i
n
A
−
s
i
n
2
A
+
1
−
s
i
n
A
−
c
o
s
A
+
s
i
n
A
c
o
s
A
s
i
n
A
(
1
−
c
o
s
A
)
+
(
1
−
s
i
n
A
)
(
1
+
c
o
s
A
)
⇒
L
H
S
=
(
c
o
s
A
+
s
i
n
A
)
−
(
c
o
s
2
A
−
s
i
n
2
A
)
+
1
−
(
c
o
s
A
+
,
s
i
n
A
)
+
s
i
n
A
c
o
s
A
s
i
n
A
(
1
−
c
o
s
A
)
+
(
1
−
s
i
n
A
)
(
1
+
c
o
s
A
)
⇒
L
H
S
=
(
c
o
s
A
+
s
i
n
A
)
−
1
+
1
−
(
c
o
s
A
+
s
i
n
A
)
+
s
i
n
A
+
c
o
s
A
s
i
n
A
(
1
−
c
o
s
A
)
+
(
1
−
s
i
n
A
)
(
1
+
c
o
s
A
)
⇒
L
H
S
=
s
i
n
A
c
o
s
A
s
i
n
A
(
1
−
c
o
s
A
)
+
(
1
−
s
i
n
A
)
(
1
+
c
o
s
A
)
=
R
H
S
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2
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