Question

[ ] is the step function. How many solution does the equation $3x=[\sin x+[\sin x+\left[\sin x\right]\left]\right]$ have in the interval $(0,2)$?

Answer 1

$3x=[\sin x+[\sin x+\left[sinx\right]\left]\right]$

for$xϵ(0,\pi /2)$ , $\sin xϵ(0,1)$

thus $\left[\sin x\right]=0$

so, $3x=0$

hence no solution

$xϵ(0,\pi /2)$

so $\sin x=0$

and $3x=0$

thus no solution exist overall