Question

Cos (A − B)

= cos (A + (−B))
= cosAcos(−B) − sinAsin(−B)

Helen is trying to prove the difference formula for cosine. She has started her proof as shown above. What property would she need to use for the next step in the proof?
A) that cosine and sine are cofunctions of each other
B) that cosine is an odd function and sine is an even function
C) that cosine is an even function and sine is an odd function
D) that cosine and sine are translations of each other by a 90° angle

Answer 1

Answer is choice C) cosine is even; sine is odd

The properties that come with even and odd functions are...
f(-x) = f(x) indicates we have an even function. So cos(-x) = cos(x)
f(-x) = -f(x) indicates we have an odd function. So sin(-x) = -sin(x)

note: the end result of the proof will lead to cos(A)cos(B)+sin(A)sin(B)