31: You should get
Now the infinity on the top is clear, but we cannot assign any limit to the
denominator due to the oscillation of cosine. Actually, there is an even
bigger problem. Note that the expression in the denominator is often zero,
namely for
The only reasonable hope lies in getting rid of that sine before we do l'Hospital's rule, that is, in combining comparison with l'Hospital. Find a suitable lower estimate for the given expression to force it up.