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Byju's Answer
Standard XII
Mathematics
Transpose of a Matrix
If A=[ cosα...
Question
If
A
=
(
cos
α
sin
α
−
sin
α
cos
α
)
,
t
h
e
n
A
10
=
A
(
cos
10
α
−
sin
10
α
sin
10
α
cos
10
α
)
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B
(
cos
10
α
sin
10
α
−
sin
10
α
cos
10
α
)
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C
(
cos
10
α
sin
10
α
−
sin
10
α
−
cos
10
α
)
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D
(
cos
10
α
−
sin
10
α
−
sin
10
α
−
cos
10
α
)
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Solution
The correct option is
C
(
cos
10
α
sin
10
α
−
sin
10
α
cos
10
α
)
A
=
[
cos
α
sin
α
−
sin
α
cos
α
]
A
2
=
A
⋅
A
=
[
cos
α
sin
α
−
sin
α
cos
α
]
⋅
[
cos
α
sin
α
−
sin
α
cos
α
]
=
[
cos
2
α
−
sin
2
α
cos
α
⋅
sin
α
+
sin
α
⋅
cos
α
−
sin
α
⋅
cos
α
−
cos
α
⋅
sin
α
−
sin
2
α
+
cos
2
α
]
=
[
cos
2
α
sin
2
α
−
sin
2
α
cos
2
α
]
Similarly,
A
10
=
[
cos
10
α
sin
10
α
−
sin
10
α
cos
10
α
]
Suggest Corrections
0
Similar questions
Q.
If the expression
4
s
i
n
5
α
c
o
s
3
α
c
o
s
2
α
is expressed as the sum of three sines then two of them are
s
i
n
4
α
and
s
i
n
10
α
. The third one is
Q.
Let
f
(
x
)
=
1
+
e
ln
(
ln
x
)
⋅
ln
(
k
2
+
25
)
and
g
(
x
)
=
1
|
x
|
−
1
. If
lim
x
→
1
f
(
x
)
g
(
x
)
=
k
(
2
sin
2
α
+
3
cos
β
+
5
)
,
k
>
0
and
α
,
β
∈
R
, then which of the following statement(s) is (are) CORRECT?
Q.
If (i)
A
=
[
cos
α
sin
α
−
sin
α
cos
α
]
, then verify that
A
′
A
=
I
(ii)
A
=
[
sin
α
cos
α
−
cos
α
sin
α
]
, then verify that
A
′
A
=
I
Q.
If
A
=
[
c
o
s
α
s
i
n
α
−
s
i
n
α
c
o
s
α
]
, then
A
2
=
Q.
If
A
=
[
cos
α
sin
α
−
sin
α
cos
α
]
, then find
A
2
.
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