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Byju's Answer
Standard XII
Mathematics
Composite Function
5sinx-12cosx=...
Question
5sinx-12cosx=-13sin3x,if
∅
=
s
i
n
−
1
(12/13), then
A
sin(2x-
ϕ
/2)=0
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B
sin(x+
ϕ
/2)=0
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C
cos(x+
ϕ
/2)=0
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D
cos(2x+
ϕ
/2)=0
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Solution
The correct option is
A
sin(2x-
ϕ
/2)=0
5
s
i
n
x
−
12
c
o
s
x
=
−
13
s
i
n
3
x
5
13
s
i
n
x
−
12
13
c
o
s
x
=
−
s
i
n
3
x
s
i
n
ϕ
=
12
13
12
13
c
o
s
x
−
5
13
s
i
n
x
=
s
i
n
3
x
s
i
n
(
ϕ
−
x
)
=
s
i
n
3
x
s
i
n
(
ϕ
−
x
)
−
s
i
n
3
x
=
0
2
c
o
s
(
ϕ
−
x
+
3
x
2
)
s
i
n
(
ϕ
−
x
−
3
x
2
)
=
0
2
c
o
s
x
(
ϕ
2
+
x
)
(
s
i
n
(
ϕ
2
−
2
x
)
)
=
0
c
o
s
(
ϕ
2
+
x
)
=
0
or
s
i
n
(
ϕ
2
−
2
x
)
=
0
Suggest Corrections
0
Similar questions
Q.
5
sin
x
−
12
cos
x
=
−
13
sin
3
x
, if
ϕ
=
sin
−
1
(
12
13
)
, then
Q.
ϕ
is an acute angle such that
tan
ϕ
=
2
3
then evaluate
(
1
+
tan
ϕ
sin
ϕ
+
cos
ϕ
)
.
(
1
−
cot
ϕ
sec
ϕ
+
csc
ϕ
)
Q.
Let
A
=
ϕ
,
ϕ
,
1
,
1
,
ϕ
,
2
. Which of the following are true?
(i)
ϕ
∈
A
(ii)
ϕ
∈
A
(iii)
1
∈
A
(iv)
2
,
ϕ
⊂
A
(v)
2
⊂
A
(vi)
2
1
⊄
A
(vii)
2
,
1
⊄
A
(viii)
ϕ
,
ϕ
,
1
,
ϕ
⊂
A
(ix)
ϕ
⊂
A
Q.
Prove that
tan
4
ϕ
+
tan
2
ϕ
=
sec
4
ϕ
−
sec
2
ϕ
, for
0
∘
≤
ϕ
≤
90
∘
Q.
Prove that the product of matrices
[
cos
2
θ
cos
θ
sin
θ
cos
θ
sin
θ
sin
2
θ
]
and
[
cos
2
ϕ
cos
ϕ
sin
ϕ
cos
ϕ
sin
ϕ
sin
2
ϕ
]
is the null matrix, when
θ
and
ϕ
differ by an odd multiple of
π
2
.
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