Find Ltx-->pi/2   {a^cot x-a^cos x}/cot x-cos x

ANS   IS     1

We have,lim a^x-1/x=lna as x tends to 0.

Now,take a^cosx common from numerator,we get,

a^cosx[a^t-1/t] where t=cotx-cosx which tends to 0 as x tends to pi/2.So,using the above result,we get the answer as a⁰.lna=lna.