The sum of all the elements in the range of where

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Solution

Q.
The sum of all the elements in the range of $f (x) = S g n (\sin x) + S g n (\cos x) + S g n (\tan x) + S g n (c o t x),$ $x \neq \frac{n π}{2}, n \in ℤ$ where $s g n (t) = {\begin{cases} 1 & i f \\ - 1 & i f \end{cases} \begin{matrix} t > 0 \\ t < 0 \end{matrix}$ is [2026]

1 4

2 -2

3 2

4 0

Ans.
(3)

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