Evaluate: lim x->0 [ tan x/sin x]

Expert Answers
justaguide eNotes educator| Certified Educator

We have to evaluate: lim x->0 [ tan x/sin x]

lim x->0 [ tan x/sin x]

=>lim x->0 [ (sin x/cos x)/sin x]

=>lim x->0 [ sin x/(cos x*sin x)]

=>lim x->0 [ 1/(cos x)]

substitute x = 0

=> 1/cos 0

=> 1/1

=> 1

The required limit is 1.