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Byju's Answer
Standard IX
Mathematics
Algebraic Identities
If A+B+C=π,...
Question
If
A
+
B
+
C
=
π
, then prove that
cos
2
A
+
cos
2
B
+
cos
2
C
=
−
1
−
4
cos
A
cos
B
cos
C
Open in App
Solution
Given:
A
+
B
+
C
=
π
L
.
H
.
S
=
cos
2
A
+
cos
2
B
+
cos
2
C
=
[
2
cos
(
A
+
B
)
cos
(
A
−
B
)
]
+
(
2
cos
2
C
−
1
)
........
cos
C
+
cos
D
=
2
cos
C
+
D
2
cos
C
−
D
2
=
2
cos
(
180
−
C
)
cos
(
A
−
B
)
+
2
cos
2
C
−
1
=
−
2
cos
C
(
cos
(
A
−
B
)
−
cos
C
)
−
1
=
−
2
cos
C
(
cos
(
A
−
B
)
+
cos
(
A
+
B
)
)
−
1
=
−
2
cos
C
(
2
cos
A
cos
B
)
−
1
=
−
4
cos
A
cos
B
cos
C
−
1
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1
Similar questions
Q.
In
Δ
A
B
C
prove:
cos
2
A
+
cos
2
B
+
cos
2
C
=
−
1
−
4
cos
A
cos
B
cos
C
Q.
Assertion (A): If
A
+
B
+
C
=
180
∘
, then
cos
2
A
+
cos
2
B
+
cos
2
C
=
1
−
2
c
o
s
A
cos
B
cos
C
.
Reason (R): If
A
+
B
+
C
=
180
∘
, then
cos
2
A
+
cos
2
B
+
cos
2
C
=
−
1
−
4
cos
A
cos
B
cos
C
.
Q.
lf
A
+
B
+
C
=
π
, then
cos
2
A
+
cos
2
B
+
cos
2
C
+
4
cos
A
cos
B
cos
C
is equal to
Q.
If A + B + C =
π
. Prove that
cos 2A + cos 2B + cos 2C = -1 -4 cos A cos B cos C.
Q.
Say true or false:
If
A
+
B
+
C
=
π
, then
cos
2
A
+
cos
2
B
+
cos
2
C
+
4
cos
A
cos
B
cos
C
is positive.
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