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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 ≠ n π 2 x\neq\frac{n\pi}{2} x = 2 nπ , where n ∈ Z n\in\mathbb{Z} n ∈ 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) f ( x ) = sgn ( sin x ) + sgn ( cos x ) + sgn ( tan x ) + sgn ( cot x )
is equal to. Here, sgn ( x ) \operatorname{sgn}(x) sgn ( x ) denotes the 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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