The number of roots of x2-2=sinx, where [.] stands for the greatest integer function, is

Given equation is x2-2=sinx.There are three possibilities:sinx=-1,sinx=0,sinx=1Case I: If sinx=-1       x2=1orx=±1When  x=1,sinx=0.But   x=-1⇒sinx=-1         x=-1is a solution.Case II: If sinx=0 the equation is       x2=2or     x±2          sin2=0  But  sin(-2)=-1.    So,  x=2  is  a  solution.Case III:  If sinx=1x=π2,5π2,9π2Clearly, these values do not satisfy the original equation.Thus, number of solutions : 2