if [sin-1x]+ [cos-1x]=0 where x is an non negativereal number and [.] denotes the greatest integer function , then complete set of values of x is -

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We havesin-1x+cos-1x=0Now domain of sin-1x and cos-1x is -1,1 but x is non-negative, hencex0,1Now x0,1 sin-1x0,π2 and cos-1xπ2,0So sin-1x+cos-1x=0 when sin-1x=0 and cos-1x=0 sin-1x=0 when x[0,sin1)  As sin-1sin1=1Similarlycos-1x=0 when x(cos1,1]  As cos-1cos1=1Taking intersection o ftwo conditions we getxcos1,sin1

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