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Byju's Answer
Standard XII
Mathematics
Sin(A+B)Sin(A-B)
Prove that ...
Question
Prove that
a
cos
A
+
b
cos
B
+
c
cos
C
=
4
R
sin
A
sin
B
sin
C
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Solution
L.H.S
=
a
cos
A
+
b
cos
B
+
c
cos
C
By sine rule
a
s
i
n
A
=
b
s
i
n
B
=
c
s
i
n
C
=
R
using trigonometric identities and simplifying
=
2
R
(
sin
A
cos
A
+
sin
B
cos
B
+
sin
C
cos
C
)
=
R
(
sin
2
A
+
sin
2
B
+
sin
2
C
)
=
2
R
(
sin
(
A
+
B
)
cos
(
A
−
B
)
−
sin
C
cos
C
)
)
=
2
R
sin
C
(
cos
(
A
−
B
)
−
cos
(
A
+
B
)
)
=
4
R
sin
A
sin
B
sin
C
=
R.H.S
Hence proved.
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Similar questions
Q.
Prove that:
a
cos
A
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B
+
c
cos
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=
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Q.
State whether the following statements are true or false:
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cos
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In ∆ ABC, prove that a cos A + b cos B + c cos C = 2a sin B sin C.
Q.
In any
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B
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cos
A
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cos
B
+
c
cos
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=
2
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sin
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.
Q.
In any
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prove that
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o
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+
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+
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Standard XII Mathematics
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