How does one evaluate the identity and prove it to be correct?
Since we don't have values for
In order to prove the identity, we must either manipulate the left hand side to be equal to the right hand side or vice versa or manipulate both sides to be equal at some middle point.
Consider the sum/difference formulas for cosine:
We will start from the left side and move to the right side:
Separating the above fraction into two fractions, we have:
Simplifying and noting that