Question

is sin(x+y) +sin(x-y)=2cosxsiny an identity?

Answer 1

add them up :)

Answer 2

$$
\sin(\color{red}x)\cos(\color{blue}y) + \cos(\color{red}x)\sin(\color{blue}y) + \sin(\color{red}x)\cos(\color{blue}y) - \cos(\color{red}x)\sin(\color{blue}y)\\
\implies
\color{green}{\pmatrix{\sin(\color{red}x)\cos(\color{blue}y) + \sin(\color{red}x)\cos(\color{blue}y)}}
+\color{green}{\pmatrix{\cos(\color{red}x)\sin(\color{blue}y)-\cos(\color{red}x)\sin(\color{blue}y)}}
$$

what do you think?

Answer 3

i don't understand what you mean?