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Byju's Answer
Standard XII
Mathematics
Trigonometric Ratios of Half Angles
If cos A +c...
Question
If
cos
A
+
cos
C
=
4
sin
2
1
2
B
, the sides
a
,
b
,
c
of the triangle are in
G
.
P
.
A
True
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B
False
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Solution
The correct option is
A
True
cos
A
+
cos
C
=
4
sin
2
B
2
b
2
+
c
2
−
a
2
2
b
c
+
a
2
+
b
2
−
c
2
2
a
b
=
4
(
s
−
c
)
(
s
−
a
)
c
a
⇒
(
b
2
+
a
c
)
(
a
+
c
)
−
(
a
3
+
c
3
)
2
a
b
c
⇒
4
(
a
+
b
−
c
)
(
b
+
c
−
a
)
(
4
)
(
c
a
)
⇒
(
b
2
+
a
c
)
(
a
+
c
)
−
(
a
3
+
c
3
)
⇒
8
b
4
(
a
b
+
a
c
−
a
2
+
b
2
+
b
c
−
a
b
−
b
c
−
c
2
+
a
c
)
⇒
(
b
2
+
a
c
)
(
a
+
c
)
−
(
a
2
+
c
3
)
⇒
8
b
4
(
−
a
4
+
b
2
−
c
2
+
2
a
c
)
⇒
(
b
2
+
a
c
)
(
a
+
c
)
−
(
a
+
c
)
(
a
2
+
c
2
−
a
c
)
⇒
2
b
(
b
2
−
(
a
−
c
)
2
)
⇒
(
a
+
c
)
(
b
2
−
(
a
2
+
c
2
−
2
a
c
)
)
⇒
2
b
(
b
2
−
(
a
−
c
)
2
)
a
+
c
=
2
b
They are in
A
.
P
Suggest Corrections
0
Similar questions
Q.
In a triangle ABC, if the sides a,b,c are roots of
x
3
−
11
x
2
+
38
x
−
40
=
0
then find the value of
cos
A
a
+
cos
B
b
+
cos
C
c
Q.
In
△
A
B
C
, if
cos
A
+
cos
C
=
4
sin
2
B
2
, then
a
,
b
,
c
(sides of the triangle) are in
Q.
STATEMENT 1: In a
Δ
A
B
C
,
if
A
,
B
,
C
are in
A
.
P
. and triangle is equilateral, then
cos
A
+
2
cos
B
+
cos
C
=
2
.
STATEMENT 2: In a
Δ
A
B
C
, if
A
,
B
,
C
are in
A
.
P
. and
cos
A
+
cos
B
+
cos
C
=
2
,
then the triangle is isosceles.
Q.
If the sides
a
,
b
,
c
are sides of a triangle
A
B
C
are roots of the equation
x
3
−
15
x
2
+
47
x
−
82
=
0
then the value of
cos
A
a
+
cos
B
b
+
cos
C
c
equal to
Q.
If
cos
A
a
=
cos
B
b
=
cos
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c
and the side
a
=
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then area of the triangle is
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