Sum and Difference Identities

\(\sin{(x+y)}=\sin{x}\cos{y}+\cos{x}\sin{y}\)

\(\sin{(x-y)}=\sin{x}\cos{y}-\cos{x}\sin{y}\)

\(\cos{(x+y)}=\cos{x}\cos{y}-\sin{x}\sin{y}\)

\(\cos{(x-y)}=\cos{x}\cos{y}+\sin{x}\sin{y}\)

\(\tan{(x+y)}=\frac{\tan{x}+\tan{y}}{1-\tan{x}\tan{y}}\)

\(\tan{(x-y)}=\frac{\tan{x}-\tan{y}}{1+\tan{x}\tan{y}}\)