Have you learned l'hopital's rule?
Been a while, but I think:
Note that if you try to evaluate the limit by substitution, you get 0/0, which is an indeterminate form. To evaluate limits with this indeterminate form, you can use l'Hopital's rule. Take the derivative of the numerator and the denominator and THEN evaluate by substitution.
Taking the derivative gives:
Evaluating this by substitution (with x = pi/2) gives the limit to be 1.