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Byju's Answer
Standard XII
Chemistry
Amino Acids
In a Δ A B C,...
Question
In a ∆ABC, if
cos
A
a
+
cos
B
b
+
cos
C
c
=
k
a
2
+
b
2
+
c
2
,
then k = ___________________.
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Solution
Using
cosine
formula
cos
A
=
b
2
+
c
2
-
a
2
2
b
c
,
cos
B
=
a
2
+
c
2
-
b
2
2
a
c
and
cos
C
=
a
2
+
b
2
-
c
2
2
a
b
L
.
H
.
S
=
cos
A
a
+
cos
B
b
+
cos
C
c
=
b
2
+
c
2
-
a
2
2
b
c
×
1
a
+
a
2
+
c
2
-
b
2
2
a
c
×
1
b
+
a
2
+
b
2
-
c
2
2
a
b
×
1
c
=
b
2
+
c
2
-
a
2
+
a
2
+
c
2
-
b
2
+
a
2
+
b
2
-
c
2
2
a
b
c
=
a
2
+
b
2
+
c
2
2
a
b
c
=
k
a
2
+
b
2
+
c
2
=
R
.
H
.
S
given
⇒
k
=
1
2
a
b
c
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