Thank you for reporting, we will resolve it shortly
Q.
If $f(x)=[\cos x]+[\sin x+1]=0$, (where [.] denotes the greatest integer function), then value of $x$ satisfying $f ( x )=0$, where $x \in[0,2 \pi]$
Trigonometric Functions
Solution:
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
$x \in\left[\frac{\pi}{2}, \pi\right) \cup\left[\frac{3 \pi}{2}, 2 \pi\right)$
