Question

Need help me prove:
Thanks!
sin (A - B) cos 2B + cos (A - B) sin 2B = sin (A + B)

Answer 1

use identities

Answer 2

note:
(A-B) + 2B = A+B

let
x = A-B
y = 2B

using angle sum identity for sine:
\[\sin(x+y) = \sin x \cos y + \cos x \sin y\]
plug back in values for x,y and you have proved the identity

Answer 3

sin (A - B) cos 2B + cos (A - B) sin 2B = sin (A + B)
LHS= sin (A - B) cos 2B + cos (A - B) sin 2B [by using sin(A+B)=sinAcosB+cosAsinB formula]
=sin(A-B+2B)
=sin(A+B)
=RHS
Thus
sin (A - B) cos 2B + cos (A - B) sin 2B = sin (A + B)

Answer 4

Thanks!