Question

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

• A. $\{0,1\}$
• B. $\{0\}$
• C. singleton set
• D. Null set

Answer 1

Answer: (C)

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