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Byju's Answer
Standard XII
Mathematics
Range
32. nbsp; ...
Question
32.
32
.
T
h
e
m
i
n
i
m
u
m
v
a
l
u
e
o
f
t
h
e
e
x
p
r
e
s
s
i
o
n
3
s
e
c
2
x
-
4
s
e
c
x
+
1
i
s
(
A
)
-
1
3
(
B
)
1
3
(
C
)
2
3
(
D
)
0
Open in App
Solution
Dear Student,
l
e
t
,
f
x
=
3
s
e
c
2
x
-
4
s
e
c
x
+
1
-
-
-
1
d
i
f
f
e
r
e
n
t
i
a
t
i
n
g
b
o
t
h
s
i
d
e
s
w
.
r
.
t
x
;
f
'
x
=
6
s
e
c
x
.
s
e
c
x
.
tan
x
-
4
s
e
c
.
tan
x
f
'
x
=
2
tan
x
3
s
e
c
2
x
-
2
s
e
c
x
p
u
t
,
f
'
x
=
0
2
tan
x
3
s
e
c
2
x
-
2
s
e
c
x
=
0
3
s
e
c
2
x
-
2
s
e
c
x
=
0
s
e
c
x
3
s
e
c
x
-
2
=
0
s
e
c
x
≠
0
D
o
e
s
n
o
t
c
o
m
e
i
n
i
t
s
r
a
n
g
e
3
s
e
c
x
-
2
=
0
→
s
e
c
x
≠
2
3
d
o
e
s
n
o
t
c
o
m
e
i
n
t
h
e
r
a
n
g
e
o
f
s
e
c
x
a
n
d
,
tan
x
=
0
→
x
=
0
n
o
w
,
s
u
b
s
t
i
t
u
t
e
t
h
e
v
a
l
u
e
o
f
x
=
0
,
i
n
1
t
o
g
e
t
m
i
n
i
m
u
m
v
a
l
u
e
o
f
t
h
e
e
x
p
r
e
s
s
i
o
n
;
S
o
,
f
0
=
3
s
e
c
2
0
-
4
s
e
c
0
+
1
=
3
-
4
+
1
=
4
-
4
=
0
Regards.
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