Hey so our professor always enjoys giving us these brain teasers at the end of each lecture, we usually tend to solve them but this one managed to confuse us all, correct me if I'm wrong I just started diving into calculus but using the theorems that we studied in limits the only approach I could think of is by using the conjugate method to somehow make the $a-cos(bx)$ to $sin$ but I believe my approach is way off, since a could be any number
Then value of 'a' has to be one or the limit would not be 0/0 and hence not exist then you can use normal procedure
Another way of going about problems of this model is writing Taylor expansions and making and making all the coefficients of terms in numerator of power less than denominator zero
Good luck for Jee if that's wt its for