Question

Number of solutions of the equation [y + [y]] = 2 $\cos$ x is
(where y = (1/3)$[\sin x+[\sin x+\left[\sin x\right]]]$ and [ ] = greatest integer function)

• A. $0$
• B. $1$
• C. $2$
• D. $\infty$

Answer 1

The correct option is A $0$

$y=\frac{1}{3}[\sin x+[\sin x+\left[\sin x\right]\left]\right]=\left[\sin x\right]\Rightarrow [y+[y\left]\right]=\cos x\therefore \left[y\right]=\cos \frac{x}{2}\Rightarrow \left[\sin x\right]=\cos x$

hence no. of solution=$0$.