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Byju's Answer
Standard XII
Mathematics
Basic Trigonometric Identities
In a triangle...
Question
In a triangle
A
B
C
,
if
B
=
30
∘
and
c
=
√
3
b
,
then show that
a^2+2b^2-3ab=0
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Solution
B
=
30
°
C
=
√
3
b
Therefore,
cos
30
°
=
c
2
+
a
2
−
b
2
2
c
a
√
3
2
=
(
√
3
b
)
2
+
a
2
−
b
2
2
√
3
b
a
3
a
b
=
(
3
b
2
−
b
2
+
a
2
)
⟹
a
2
+
2
b
2
−
3
a
b
=
0
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0
Similar questions
Q.
If
a
3
+
b
3
+
c
3
=
3
a
b
c
and
a
+
b
+
c
=
0
show that
(
b
+
c
)
2
3
b
c
+
(
c
+
a
)
2
3
a
c
+
(
a
+
b
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2
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a
b
=
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Q.
In a triangle ABC if
a
4
−
2
(
b
2
+
c
2
)
a
2
+
b
4
+
b
2
c
2
+
c
4
=
0
then show
∠
A
is
60
∘
or
120
∘
Q.
If
a
2
+
c
2
=
2
b
2
where a, b, c are the sides of a triangle, then prove that
s
i
n
3
B
s
i
n
B
=
[
a
2
−
c
2
2
a
c
]
2
Q.
Let
sin
x
and
sin
y
be roots of the quadratic equation
a
sin
2
θ
+
b
sin
θ
+
c
=
0
(
a
,
b
,
c
∈
R
and
a
≠
0
)
such that
sin
x
+
2
sin
y
=
1
, then the value of
(
a
2
+
2
b
2
+
3
a
b
+
a
c
)
equals
Q.
If in a triangle ABC,
sin
A
sin
C
=
sin
(
A
−
B
)
sin
(
B
−
C
)
, then show that
a
2
,
b
2
,
c
2
are in A.P.
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