Answer:
see explanation
Step-by-step explanation:
Using the Addition/ Subtraction formulae for cosine
Consider the left side
cos(x - y) - cos(x + y)
= cosxcosy + sinxsiny - (cosxcosy - sinxsiny) ← distribute
= cosxcosy + sinxsiny - cosxcosy + sinxsiny ← collect like terms
= 2sinxsiny = right side ⇒ proven
