The value of $[\sin x]+[1 + \sin x] + [2+ \sin x]$ in $x∈(π, 3π/2]$ can be ([-] is the greatest integer function) can be.
Answer & explanation
Correct answer: option 1
We have,
$[\sin x]+[1 + \sin x] + [2 + \sin x]$
$= [\sin x]+1+[\sin x] + 2 + [\sin x]$
$= 3+3 [\sin x]$
$=3+ 3× (-1)=0$ $[∵ [\sin x] = -1\, for\, x ∈ (π, 3π/2]$