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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?)