When proving identities, we have the option to work on both sides of the identity.Group of answer choicesTrueFalse

Final Answer

True

Explanation

In mathematical proofs, particularly when working with identities, it is indeed valid to manipulate both sides of the identity. This technique is often utilized to demonstrate that two expressions are equivalent. The strategy involves starting from one side, applying algebraic manipulations or known identities, and transforming it into the form of the other side.

For example, if we are tasked with proving that $A \equiv B$, we can start by taking $A$ and simplifying or rearranging it using algebraic identities, properties, or transformations until we arrive at $B$. Conversely, we could also start with $B$ and try to manipulate it to match $A$.

This flexibility allows mathematicians to approach the proof from various angles, which can often lead to clearer and more straightforward solutions. Just remember to be logical and ensure that all operations performed are valid and maintain the equality.