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Question
Mathematics
If A= [cos2 α&cos α sin α cos α sin α&sin2 α] and B= [cos2 β &cos β sin β cos β sin β &sin2 β ] are two matrices such that the product AB is null matrix, then α -β is
Q. If
A
=
[
co
s
2
α
cos
α
s
in
α
cos
α
s
in
α
s
i
n
2
α
]
and
B
=
[
co
s
2
β
cos
β
s
in
β
cos
β
s
in
β
s
i
n
2
β
]
are two matrices such that the product
A
B
is null matrix, then
α
−
β
is
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A
0
B
multiple of
π
C
an odd multiple of
π
/2
D
None of the above
Solution:
Given,
A
B
=
O
∴
[
co
s
2
α
cos
α
s
in
α
cos
α
s
in
α
s
i
n
2
α
]
×
[
co
s
2
β
cos
β
s
in
β
cos
β
s
in
β
s
i
n
2
β
]
=
[
0
0
0
0
]
[
cos
α
cos
β
cos
(
α
−
β
)
cos
β
s
in
α
cos
(
α
−
β
)
cos
α
s
in
β
cos
(
α
−
β
)
s
in
α
s
in
β
cos
(
α
−
β
)
]
=
[
0
0
0
0
]
⇒
cos
(
α
−
β
)
=
0
⇒
α
−
β
is an odd multiple of
π
/2