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Byju's Answer
Standard XIII
Mathematics
General Solutions of (sin theta)^2 = (sin alpha)^2 , (cos theta)^2 = (cos alpha)^2 , (tan theta)^2 = (tan alpha)^2
The inequalit...
Question
The inequality
2
cos
x
≤
∣
∣
√
1
+
sin
2
x
−
√
1
−
sin
2
x
∣
∣
≤
√
2
where
x
∈
[
0
,
2
π
]
holds true in the interval
[
a
π
2
,
b
π
2
]
. Then the value of
a
+
b
is
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Solution
∣
∣
√
1
+
sin
2
x
−
√
1
−
sin
2
x
∣
∣
=
∣
∣
∣
|
cos
x
+
sin
x
|
−
|
cos
x
−
sin
x
|
∣
∣
∣
=
2
min
{
|
cos
x
|
,
|
sin
x
|
}
Now,
2
cos
x
≤
2
min
{
|
cos
x
|
,
|
sin
x
|
}
≤
√
2
⇒
cos
x
≤
min
{
|
cos
x
|
,
|
sin
x
|
}
≤
1
√
2
Clearly, from the graph,
x
∈
[
π
4
,
7
π
4
]
a
+
b
=
1
2
+
7
2
=
4
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Similar questions
Q.
The inequality
2
cos
x
≤
∣
∣
√
1
+
sin
2
x
−
√
1
−
sin
2
x
∣
∣
≤
√
2
where
x
∈
[
0
,
2
π
]
holds true in the interval
[
a
π
2
,
b
π
2
]
. Then the value of
a
+
b
is
Q.
Determine all the values of
x
in the interval
x
ϵ
[
0
,
2
π
]
which satisfy the inequality
2
cos
x
≤
∣
∣
√
1
+
sin
2
x
−
√
1
−
sin
2
x
∣
∣
≤
2
Q.
The solution of the equation
(
sin
x
+
cos
x
)
1
+
sin
2
x
=
2
,
−
π
≤
x
≤
π
, is
Q.
If sin (sin
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Q.
The range of
x
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3
sin
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[
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3
−
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x
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)
]
holds is :
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General Solutions of (sin theta)^2 = (sin alpha)^2 , (cos theta)^2 = (cos alpha)^2 , (tan theta)^2 = (tan alpha)^2
Standard XIII Mathematics
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