What is the difference between a conditional equation and an identity?

Question

Give an example for each of them.

Answer 1

A conditional equation in the variable x is an equation that is satisfied by some, but not all values of x for which both sides of the equation are defined.  

               Example:  sinx = cosx

 

An identity in the variable x is an equation that is satisfied by all values of x for which both sides of the equation are defined.  

 

               Example:  tanx = sinx/cosx