Question

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.

Answer 1

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)

Answer 2

cos (A-B) - cos (A+B)
= (cosAcosB +sinAsinB) - (cosAcosB - sinAsinB)
=2sinAsinB

Ans: 4