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Byju's Answer
Standard XII
Mathematics
General Solution of Trigonometric Equation
In ABC sin...
Question
In
△
A
B
C
sin
(
A
−
B
)
sin
(
A
+
B
)
=
a
2
−
b
2
c
2
A
True
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B
False
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Solution
The correct option is
A
True
In
Δ
A
B
C
From
sin
rule
a
=
2
R
sin
A
,
b
=
2
R
sin
B
,
c
=
2
R
sin
C
Consider
sin
(
A
−
B
)
sin
(
A
+
B
)
Multiplying and dividing by
sin
(
A
+
B
)
⟹
sin
(
A
+
B
)
sin
(
A
−
B
)
sin
2
(
A
+
B
)
⟹
(
sin
2
A
−
sin
2
B
)
sin
2
(
π
−
C
)
⟹
(
sin
2
A
−
sin
2
B
)
sin
2
C
⟹
a
2
−
b
2
c
2
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0
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Q.
In
△
A
B
C
,
s
i
n
(
A
−
B
)
s
i
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(
A
+
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)
=
[MP PET 1986]
Q.
If in any triangle
A
B
C
;
a
2
−
b
2
a
2
+
b
2
=
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(
A
−
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)
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(
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+
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)
, then the triangle is
Q.
If in
△
A
B
C
,
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A
sin
C
=
sin
(
A
−
B
)
sin
(
B
−
C
)
,
Prove that
a
2
,
b
2
,
c
2
are in
A
.
P
.
Q.
In any
Δ
A
B
C
, prove that
a
2
−
b
2
c
2
=
sin
(
A
−
B
)
sin
(
A
+
B
)
.
Q.
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