Sum to Product

Question 1

What is cos(A) + cos(B) equal to?

Answer 1

cos(A) + cos(B) = 2 cos[(A + B)/2] cos[(A − B)/2]

Question 2

What is cos(A) − cos(B) equal to?

Answer 2

cos(A) − cos(B) = −2 sin[(A + B)/2] sin[(A − B)/2]

Question 3

What is sin(A) + sin(B) equal to?

Answer 3

sin(A) + sin(B) = 2 sin[(A + B)/2] cos[(A − B)/2]

Question 4

What is sin(A) − sin(B) equal to?

Answer 4

sin(A) − sin(B) = 2 cos[(A + B)/2] sin[(A − B)/2]