The sum of all the elements in the range of \(f\left(x\right)=\text{Sgn}\left(\sin x\right)+\text{ Sgn}\left(\cos x\right)+\)\(\text{Sgn}\left(\tan x\right)+\text{Sgn}\left(\cot x\right)\), \(x\text{ }\neq \text{ }\frac{n\text{ }\pi }{2},\text{ }n\text{ }\in \text{ }Z,\) where \(\text{Sgn}\left(t\right)=\left{\begin{matrix}1, & \text{if} & t\text{ }>\text{ }0 \\ −1 & \text{if} & t\text{ }<\text{ }0\end{matrix},\right.\) is:

[JEE Main 2026, 28 Jan (Shift 2)]

Question

The sum of all the elements in the range of \(f\left(x\right)=\text{Sgn}\left(\sin x\right)+\text{ Sgn}\left(\cos x\right)+\)\(\text{Sgn}\left(\tan x\right)+\text{Sgn}\left(\cot x\right)\), \(x\text{ }\neq \text{ }\frac{n\text{ }\pi }{2},\text{ }n\text{ }\in \text{ }Z,\) where \(\text{Sgn}\left(t\right)=\left{\begin{matrix}1, & \text{if} & t\text{ }>\text{ }0 \\ −1 & \text{if} & t\text{ }<\text{ }0\end{matrix},\right.\) is:

[JEE Main 2026, 28 Jan (Shift 2)]

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