Question

The number of solutions of the equation
$\left[\sin x\right]=\cos x\forall x\in [0,2\pi ]$ (where $\left[\right]$ denotes the greatest integer function)

• A. $3$
• B. $0$
• C. $2$
• D. $4$

Answer 1

The correct option is B $0$

$\cos x=\left[\sin x\right]$
$\cos x=-1,0,1$ as $-1\le \cos x\le 1$
$x=\pi .\pi /2.2\pi \therefore \left[\sin x\right]=0,1,0$
so equation $\left[\sin x\right]=\cos x$ has no solution

Thus option B is the correct answer.