The conditions of two functions being equal:

(1)Ranges should be equal

(2)Codomains should be equal

Now my doubt is, let one function be sinx and the other be cosx,then we have the ranges and the codomains of both the functions to be equal.But these are not equal functions.Please explain it.

THE DIFFERENCE LIE BETWEEN THE CORRESPONDING VALUES........FOR EVERY SAME VALUE OF (X) ,(Y) HAS DIFFERNT VALUES IN CASE OF COSX AND SINX......WE  ARE LIMITING OUR SELVES IN 0 TO PIE.....

EXCEPT FOR PIE/4 ALL THE ORDERED PAIRS FROM SETX TO SETY ARE DIFFERENT THAT'S WHY THESE FUNCTIONS ARE ALSO DIFFERENT.......

Yes,I have underatood.So the definition needs to be corrected.