Question

Prove the identity.
show steps please

Answer 1

\[\tan(y)={((\sin(x+y))-\sin(x-y))} / {(\cos(x+y)+\cos(x-y)}\]

Answer 2

\[\sin{(x\pm y)}=\sin{x}\cos{y}\pm\cos{x}\sin{y}\]\[\cos{(x\pm y)}=\cos{x}\cos{y}\mp\sin{x}\sin{y}\]\[\frac{\sin{(x+y)}-\sin{(x-y)}}{\cos{(x+y)}+\cos{(x-y)}}=\frac{2\cos{x}\sin{y}}{2\cos{x}\cos{y}}=\tan{y}\]

Answer 3

thank you!!!