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  4. Range of f ( x )=[| sin x |+| cos x |] ∀ x ∈ R where [ ] denotes the greatest integer function, is

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Q. Range of $f ( x )=[|\sin x |+|\cos x |] \forall x \in R$ where [ ] denotes the greatest integer function, is

Relations and Functions - Part 2

Solution:

$\text { Range of } y=|\sin x|+\mid \cos x $
$\Rightarrow y^2=1+|\sin 2 x|$
$y^2=\in[1,2] $
$y \in[1, \sqrt{2}], y >0$
Range of $y=[|\sin x|+|\cos x|]=1$