relationship between sin and cos

Question

7. Give the formula for cos (x − y) in terms of cos x,
sin x,sin y, and cos y.
Answer:
cos x cos y + sin x sin y

 

I don't get the question, what am I supposed to be checking? is there a specific relationship between sin and cos that I need to understand to do this problem? I'm just lost. Thanks

Answer 1

The formula Cos(X-Y)=CosxCosy+SinxSiny may be proved by the relationship of angle x and angle y inscribed within the unit circle. This format does not provide the means to develop the proof but if you wish to respond with an email address I will send you a copy of my proof for the formula.