For , where , the range of the function f(x)= sgn ( x)+ sgn ( x)+ sgn ( x)+ sgn ( x)…

MATHEMATICS · Single correct · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

For x≠nπ2x\neq\frac{n\pi}{2}, where n∈Zn\in\mathbb{Z}, the range of the function f(x)=sgn⁡(sin⁡x)+sgn⁡(cos⁡x)+sgn⁡(tan⁡x)+sgn⁡(cot⁡x)f(x)=\operatorname{sgn}(\sin x)+\operatorname{sgn}(\cos x)+\operatorname{sgn}(\tan x)+\operatorname{sgn}(\cot x) is equal to. Here, sgn⁡(x)\operatorname{sgn}(x) denotes the signum function of xx. (a) {−2,4}\{-2,4\} (b) {−2,0,4}\{-2,0,4\} (c) {−4,−2,0,4}\{-4,-2,0,4\} (d) {0,2,4}\{0,2,4\}

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