Please Help:

Question

please solve this proof:

cosx- cosy = -2sin(x+y/2)sin(x-y/2)

Answer 1

let (x+y)/2 = A ---> x+y=2A
let (x-y)/2 = B ---> x-y=2B

adding those : 2x = 2A + 2B
then x = A+B and similarly
y = A - B

so your identity becomes

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

LS
= cosAcosB - sinAsinB -(cosAcosB + sinAsinB)
= -2sinAsinB
= -2sin(x+y/2)sin(x-y/2)
= RS

Answer 2

Thanks so much for the help=)