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Byju's Answer
Standard XII
Mathematics
Cos(A+B)Cos(A-B)
If A+B+C=π ...
Question
If
A
+
B
+
C
=
π
and
cos
A
=
cos
B
.
cos
C
then show that
cot
B
cot
C
=
1
2
.
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Solution
Let us consider the problem.
Let
A
+
B
+
C
=
180
0
degrees
Hence
A
=
180
0
−
(
B
+
C
)
Therefore
cos
A
=
cos
B
+
cos
C
Implies that
cos
(
180
0
−
B
−
C
)
=
cosBcosC
implies that
−
cos
(
B
+
C
)
=
cos
B
.
cos
C
Implies that
−
cos
B
cos
C
+
sin
B
sin
C
=
cos
B
.
cos
C
Implies that
2
cos
B
cos
C
=
sin
B
sin
C
Implies that
Hence
cot
B
cot
C
=
1
2
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