This is because when we do verification of an
identity, we must work separately on both sides, and to see in the end
if we can get an equality. Because if we square both sides, that already means
that we assume that the equality exist in the beginning, so no need to
verify the identity.
While we are proving or verifying a trigonometric identity, we do not need to square each side of the equation.
This is so because if we are squaring each side of the equation, It means that the identity already exists and there is nothing to prove then.
So, we can only take one side and manipulate it or solve in such a way to reach a expression which is equivalent to the other. But we cannot square the both sides simultaneously because we don't know whether the identity holds or not, We are just verifying it whether it is true or not.
Hence, If we square each side of the equation then there is no use of proving or verifying the identity,
