Google it and you will find the answer.
lim x->0 sin(x)/x=1 lim x->0 1-cos(x)/x=0
http://answers.yahoo.com/question/index?qid=20080603183843AAHFO2l
lim->0 x+tan(x)/sin(x)
lim 1/ (x/sinx + tanx/sinx)
note:
lim sinx/x = 1
thus
lim x/sinx = 1
now, tanx / sinx = 1/cosx .
and lim (1/cos(x)) = 1, as x→0
thus
lim sinx/(x+ tanx) = 1/(1 + 1) = 1/2
(Is that the trig proof and answer?)