The expression cos (A-B) - cos (A+B) is equal to

1) - 2sinAsinB

2) - 2cosB

3) 2cosAcosB

4) 2sinAsinB

So far, all I've gotten is

cosxcosy + sinxsiny - cosxcosy - sinxsiny

I don't know where to go from there. I'm assuming that's zero, and I don't know which of the others equal 0 ... they all look the same.

Cos (A+B) = cos (A) cos (B) - sin (A) sin (B)

cos (A-B) = cos (A) cos (B) + sin (A) sin (B)

Then:

cos (A-B) - cos (A+B) =

[cos (A) cos (B) + sin (A) sin (B) ]-[cos (A) cos (B) - sin (A) sin (B) ]=

cos (A) cos (B) + sin (A) sin (B) - cos (A) cos (B) + sin (A) sin (B) =

sin (A) sin (B) + Sin (A) sin (B) =

2sin (A) sin (B)

Answer: 4) 2sin (A) sin (B)

Cos (A-B) - cos (A+B)

= (cosAcosB + sinAsinB) - (cosAcosB - sinAsinB)

=2sinAsinB

Ans: 4