Question

If $f(x)=[\cos x]+[\sin x+1]=0$, (where [.] denotes the greatest integer function), then value of $x$ satisfying $f(x)=0$, where $x\in [0,2\pi ]$

• A. $x\in (\pi /2,\pi ]\cup [3\pi /2,2\pi ]$
• B. $x\in (0,\pi /2)$
• C. $x\in [\pi /2,\pi ]\cup [3\pi /2,2\pi ]$
• D. $x\in [\pi ,2/\pi ]$

Answer 1

Answer: (A)

Given equation can be written as $[\cos x]+[\sin x]+1=0$
$[\sin x]+[\cos x]=-1...(i)$
Now draw is graphs of $[\cos x]+[\sin x]$

From graph it is clear that equation (i) is satisfied for
$x\in \left[\frac{\pi }{2},\pi \right)\cup \left[\frac{3\pi }{2},2\pi \right)$