Evaluate limx→0tan(tanx)−sin(sinx)tanx−sinx
First I tried using L'Hopital's rule..but it's very lengthy
Next I have written the limits as
L=limx→0tan(tanx)−sin(sinx)tanx−sinx=limx→0tan(tanx)−sin(sinx)x3limx→0tanx−sinxx3=L1L2
Now by L'Hopital's Rule we get L2=0.5
L1=limx→0tan(tanx)−sin(sinx)x3
Now L1 can also be evaluated using three applications of L'Hopital's Rule, but is there any other approach?
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