What is an Identity?
Consider the equality we shall evaluate both sides of this equality for some value of a, say a = 10
The values of the two sides of the equality are equal for a = 10.
Let us now take a = -1
For a = -1, LHS = RHS
We shall find that for any value of a, LHS = RHS. Such an equality, which is true for every value of the variable in it, is called an identity. Thus
is an identity.
An equation is true for only certain values of the variables in it. It is not true for all values of the variable.
is true for a = 10. But it is not true for a = -1 or a = 0 etc.