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Problem
Problem
For
x
≠
n
π
2
x \neq \frac{n\pi}{2}
x
=
2
nπ
where
n
∈
I
n \in I
n
∈
I
, the range of function
f
(
x
)
=
sgn
(
sin
x
)
+
sgn
(
cos
x
)
+
sgn
(
tan
x
)
+
sgn
(
cot
x
)
f(x) = \text{sgn}(\sin x) + \text{sgn}(\cos x) + \text{sgn}(\tan x) + \text{sgn}(\cot x)
f
(
x
)
=
sgn
(
sin
x
)
+
sgn
(
cos
x
)
+
sgn
(
tan
x
)
+
sgn
(
cot
x
)
is equal to Note:
sgn
x
\text{sgn } x
sgn
x
denotes signum function of
x
x
x
. (a)
{
−
2
,
4
}
\{-2, 4\}
{
−
2
,
4
}
(b)
{
−
2
,
0
,
4
}
\{-2, 0, 4\}
{
−
2
,
0
,
4
}
(c)
{
−
4
,
−
2
,
0
,
4
}
\{-4, -2, 0, 4\}
{
−
4
,
−
2
,
0
,
4
}
(d)
{
0
,
2
,
4
}
\{0, 2, 4\}
{
0
,
2
,
4
}
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