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Byju's Answer
Standard XII
Mathematics
Equations Involving sinx + cosx and sinx.cosx
If the equati...
Question
If the equation
sin
4
x
−
(
k
+
2
)
sin
2
x
−
(
k
+
3
)
=
0
has a solution, then
k
must lie in the interval
A
(
−
4
,
−
2
)
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B
[
−
3
,
2
)
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C
(
−
4
,
−
3
)
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D
[
−
3
,
−
2
)
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Solution
The correct option is
D
[
−
3
,
−
2
)
S
i
n
4
x
−
(
k
+
2
)
s
i
n
2
x
−
(
k
+
3
)
=
0
Let
s
i
n
2
x
=
y
y
2
−
(
k
+
2
)
y
−
k
+
3
=
0
y
=
k
+
2
±
√
(
k
+
2
)
2
+
4
(
k
+
3
)
2
y
=
k
+
2
±
√
k
2
+
4
+
4
k
+
12
2
y
=
k
+
2
±
√
k
2
+
8
k
+
16
2
y
=
(
k
+
2
)
±
k
+
4
2
y
=
k
+
2
−
k
−
4
2
;
y
=
k
+
2
+
k
+
4
2
y
=
−
1
,
y
=
k
+
3
s
i
n
2
x
=
−
1
s
i
n
2
x
=
k
+
3
Not possible
s
i
n
x
=
√
k
+
3
(
∵
It is given that
the ep. has sol)
0
≤
s
i
n
x
≤
1
s
i
n
x
=
0
0
=
k
+
3
k
=
−
3
Min value of
k
=
−
3
s
i
n
x
=
1
1
=
k
+
3
−
2
=
k
Max value of
k
=
−
2
∴
k
l
i
e
s
i
n
i
n
t
e
r
v
a
l
[
−
3
,
−
2
)
Suggest Corrections
0
Similar questions
Q.
If the equation
sin
4
x
−
(
k
+
2
)
sin
2
x
−
(
k
+
3
)
=
0
has a solution then k must lie in the interval
Q.
If the equation
sin
4
x
−
(
k
+
2
)
sin
2
x
−
(
k
+
3
)
=
0
has a solution then
k
must lie in the interval:
Q.
The equation
sin
4
x
+
cos
4
x
+
sin
2
x
+
k
=
0
must have real solutions if
Q.
The equation
sin
4
x
−
(
k
+
2
)
sin
2
x
−
(
k
+
3
)
=
0
possesses a solution if
Q.
If
f
(
x
)
=
x
3
+
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x
2
+
kx
+
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is a monotonically decreasing function of x in the largest possible interval (-2, -2/3). Then
.