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Byju's Answer
Standard XII
Mathematics
Composition of Trigonometric Functions and Inverse Trigonometric Functions
The smallest ...
Question
The smallest value of θ satisfying the equation
3
cot
θ
+
tan
θ
=
4
is
(a)
2
π
/
3
(b)
π
/
3
(c)
π
/
6
(d)
π
/
12
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Solution
(c)
π
/
6
Given:
3
(
cot
θ
+
tan
θ
)
=
4
⇒
3
cos
θ
sin
θ
+
sin
θ
cos
θ
=
4
⇒
3
(
cos
2
θ
+
sin
2
θ
)
=
4
sin
θ
cos
θ
⇒
3
=
2
sin
2
θ
[
sin
2
θ
=
2
sin
θ
cos
θ
]
⇒
sin
2
θ
=
3
2
⇒
sin
2
θ
=
sin
π
3
⇒
2
θ
=
n
π
+
(
-
1
)
n
π
3
,
n
∈
Z
⇒
θ
=
n
π
2
+
(
-
1
)
n
π
6
,
n
∈
Z
To obtain the smallest value of
θ
, we will put
n
=
0
in the above equation.
Thus, we have:
θ
=
π
6
Hence, the smallest value of
θ
is
π
6
.
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Similar questions
Q.
The smallest value of x satisfying the equation
3
cot
x
+
tan
x
=
4
is
(a)
2
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/
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(b)
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/
3
(c)
π
/
6
(d)
π
/
12
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Angle between asymptotes of the hyperbola
3
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Q.
The smallest positive value of
θ
' satisfying the equation
√
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(
c
o
t
θ
+
t
a
n
θ
)
=
4
is
Q.
If
cos
θ
+
3
sin
θ
=
2
,
then
θ
=
(a)
π
/
3
(b)
2
π
/
3
(c)
4
π
/
6
(d)
5
π
/
12
Q.
Assertion :The value of
θ
,
0
<
θ
<
π
2
,
satisfying the equation
6
∑
m
=
1
c
o
s
e
c
[
θ
+
(
m
−
1
)
π
4
]
c
o
s
e
c
[
θ
+
m
π
4
]
=
4
√
2
are
π
12
and
5
π
12
Reason: If
tan
θ
+
cot
θ
=
4
,
0
<
θ
<
π
2
,
then
θ
=
π
12
or
5
π
12
.
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