lim(1-√(cosx))/(√(1+xsinx)-√(cosx))
=lim(1-cosx)(√(1+xsinx)+√(cosx))/(1+xsinx-cosx)(1+√cosx)
=lim(1-cosx)/(1+xsinx-cosx)
=lim(x^2/2)/(xsinx+x^2/2)
=1/3