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Byju's Answer
Standard XII
Mathematics
Integration Using Substitution
State whether...
Question
State whether the given statement is true or false
1
+
cot
θ
≥
cot
θ
/
2
for
0
<
θ
<
π
. Find
θ
when equality signs holds.If this is true enter 1, else enter 0.
A
True
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B
False
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Solution
The correct option is
B
False
Given,
1
+
cos
θ
sin
θ
≥
cos
θ
2
sin
θ
2
sin
θ
+
cos
θ
sin
θ
≥
cos
θ
2
sin
θ
2
sin
θ
+
cos
θ
2
sin
θ
2
.
cos
θ
2
≥
cos
θ
2
sin
θ
2
sin
θ
+
cos
θ
2
sin
θ
2
.
cos
θ
2
−
2
cos
2
θ
2
2
sin
θ
2
.
cos
θ
2
≥
0
1
sin
θ
[
sin
θ
+
cos
θ
−
(
1
+
cos
θ
)
]
≥
0
c
o
s
e
c
θ
[
s
i
n
θ
−
1
]
≥
0
1
−
c
o
s
e
c
θ
≥
0
1
≥
c
o
s
e
c
θ
sin
θ
≥
1
sin
θ
=
1
or
sin
θ
>
1
But,
|
sin
θ
|
≤
1
Hence,
sin
θ
=
1
θ
=
π
2
.
Suggest Corrections
0
Similar questions
Q.
State whether the given statement is true or false
√
1
+
sin
θ
1
−
sin
θ
=
sec
θ
−
tan
θ
,
−
π
2
<
θ
<
π
2
.
Q.
Eliminate
θ
, if
x
=
3
c
o
s
e
c
θ
+
4
c
o
t
θ
,
y
=
4
c
o
s
e
c
θ
−
3
c
o
t
θ
Answer:
(
3
x
+
4
y
)
2
−
(
4
x
−
3
y
)
2
=
625
If true then enter 1 else if False enter 0
Q.
sin
θ
=
cos
θ
for all values of
θ
Enter
1
for true and
0
for false
Q.
State whether the g
iven equation is true or false:
cot
θ
+
c
o
s
e
c
θ
−
1
cot
θ
−
cosec
θ
+
1
=
cot
θ
2
Q.
For any acute angle
θ
(
sin
θ
)
increases as
θ
increases
If true then enter
1
and if false then enter
0
.
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