How can I use the "angle addition formula" and the formula "limit of x approaching 0 of sin(x)" to show that the limit of x approaching 0 sin(a+x) = sin(a) for all a?

Answer 1

sin (a+x) = sin a cos x + sin x cos a
As x-> 0, cos x -> 1 and sin a -> 0
Therefore sin (a+x) approaches sin a