Question

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

Answer 1

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

Ans: 4

Answer 2

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)