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Question
Mathematics
The expression cos 2(A-B)+ cos 2 B-2 cos (A-B) cos A cos B is independent of
Q. The expression
cos
2
(
A
−
B
)
+
cos
2
B
−
2
cos
(
A
−
B
)
cos
A
cos
B
is independent of
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231
Bihar CECE
Bihar CECE 2009
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A
A
B
B
C
both A and B
D
neither A nor B
Solution:
cos
2
(
A
−
B
)
+
cos
2
B
−
2
cos
(
A
−
B
)
cos
A
cos
B
=
cos
2
(
A
−
B
)
+
cos
2
B
−
cos
(
A
−
B
)
[
cos
(
A
+
B
)
+
cos
(
A
−
B
)]
=
cos
2
B
−
cos
(
A
−
B
)
cos
(
A
+
B
)
=
cos
2
B
−
2
1
[
cos
2
A
+
cos
2
B
]
=
cos
2
B
−
2
1
[
2
cos
2
B
−
1
+
cos
2
A
]
=
2
1
−
2
1
cos
2
A
=
2
1
−
2
1
(
2
cos
2
A
−
1
)
=
1
−
cos
2
A
=
sin
2
A
Hence, it is independent of
B
.