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

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justaguide | College Teacher | (Level 2) Distinguished Educator

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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.

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