lim x趋于0 ,(根号下一加tanx减 根号下一加sinx ) 除以 (x乘以根号下一加sinx平方减x)

lim(√1+tanx-√1+sinx)/(x√1+sinx^2-x)
x->0
=lim(1+tanx-1-sinx)(lim(√1+tanx-√1+sinx)/(x√1+sinx^2-x)
x->0
=lim(1+tanx-1-sinx)(√1+sinx^2+1)/[(√1+tanx+√1+sinx)x(1+sinx^2-1)
x->0
=lim 2(tanx-sinx)/(2xsinx^2)
x->0
=lim(1-cosx)/(xsinxcosx)
x->0
=lim(2sin(x/2)^2/(x^2)
x->0
=8lim sin(x2/2)^2/(x/2)^2
x->0
=8