Question

Verify the identity.

sin (x + y) - sin (x - y) = 2 cos x sin y

Answer 1

use Sum and Difference Identity :
sin(x±y) = sinxcosy ± cosysinx

Answer 2

oh okay! thank you! give me a minute to see if I can get teh answer

Answer 3

\[2cosxsiny=sinxcosy+cosxsiny-sinxcosy+cosxsiny\]
\[2cosxsiny=2cosxsiny\]

Answer 4

or you can also substitute sin(x±y) = sinxcosy ± cosysinx

sin (x + y) - sin (x - y) = 2 cos x sin y
(sin x cos y + cos y sin x) - (sin x cos y - cos y si nx) =
(sin x cos y - sin x cos y + cos y sin x + cos y sin x) =
∴ 2 cos x sin y = 2 cos x sin y

:-)