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Byju's Answer
Standard XII
Physics
Vector Component
If in a trian...
Question
If in a triangle
A
B
C
,
θ
is the angle determined by
c
o
s
θ
=
(
a
−
b
)
/
c
,
then which of the following is correct?
A
(
a
+
b
)
sin
θ
2
√
a
b
=
cos
A
−
B
2
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B
(
a
+
b
)
sin
θ
2
√
a
b
=
cos
A
+
B
2
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C
c
sin
θ
2
√
a
b
=
cos
A
−
B
2
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D
c
sin
θ
2
√
a
b
=
cos
A
+
B
2
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Solution
The correct options are
C
c
sin
θ
2
√
a
b
=
cos
A
+
B
2
D
(
a
+
b
)
sin
θ
2
√
a
b
=
cos
A
−
B
2
cos
θ
=
(
a
−
b
c
)
sin
θ
=
√
1
−
(
a
−
b
)
2
c
2
=
1
c
√
c
2
−
(
a
−
b
)
2
(A)
(
a
+
b
)
sin
θ
2
√
a
b
⇒
(
a
+
b
)
2
×
√
a
b
×
c
√
c
2
−
(
a
−
b
)
2
⇒
(
a
+
b
)
2
√
a
b
×
c
√
(
a
2
+
b
2
−
c
2
)
+
2
a
b
=
(
a
+
b
)
2
√
a
b
×
c
√
2
a
b
(
1
−
cos
c
)
⇒
(
a
+
b
)
√
2
×
c
×
√
2
sin
(
c
2
)
=
sin
A
+
sin
B
sin
C
×
sin
(
c
2
)
=
2
sin
(
A
+
B
2
)
cos
(
A
−
B
2
)
2
sin
(
c
2
)
cos
(
c
2
)
sin
(
c
2
)
=
cos
(
A
−
B
2
)
Hence,
(
a
+
b
)
sin
θ
2
√
a
b
=
cos
(
A
−
B
2
)
is correct.
(D)
c
√
c
2
−
(
a
−
b
)
2
2
√
a
b
⇒
c
×
√
2
a
b
(
1
−
cos
c
)
2
√
a
b
×
c
⇒
sin
c
2
⇒
cos
A
+
B
2
Hence,
c
sin
θ
2
√
a
b
=
cos
A
+
B
2
is correct.
Suggest Corrections
0
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