Expert: Paul Klarreich - 12/11/2011

Question
how can we prove lim sinx= sina when x approach to a

Answer
Questioner: bektur
Country: Istanbul, Turkey
Category: Calculus
Private: Yes <<<<  changed
Subject: limit of sinx
Question: how can we prove lim sinx = sina when x approach to a

See : http://en.wikipedia.org/wiki/List_of_trigonometric_identities

for

sin x - sin a = 2 sin( (x-a)/2 ) cos( (x+a)/2 )

Now as x -> a:  x - a -> 0,  so  sin( (x-a)/2 ) -> sin(0) = 0
and as x -> a:  x + a -> 2a, so  cos( (x+a)/2 ) -> cos(a)

Thus

sin x - sin a -> 2[ 0 ][ cos a] = 0

That should do it.