Question 1209180
.



        As I read your post, it is unclear to me, is it a statement or a question.


        But, taking into account, that half of the posts at this forum are mathematically 
        and grammatically incorrect and require to be fixed, 
        I will assume that it is a question of the type "True or False".



The given function is identically equal to -1 everywhere in vicinity of x = pi/2
and is not defined at x = pi/2.


Therefore, if to define it as -1 at x= pi/2, you will get a continuous function at x= pi/2.