Evaluate $lim_(x->0) (tanx-sinx)/(xcosx)$ ?

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How do you evaluate $lim_(x->0) (tanx-sinx)/(xcosx)$ ?

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Answer 1 · 2018-03-24T18:46:54

$0$ .

$lim_(x to 0)(tanx-sinx)/(xcosx)$ ,

$=lim{sinx/cosx-sinx}/(xcosx)$ ,

$=lim(sinx-sinxcosx)/(xcos^2x)$ ,

$=limsinx/x*(1-cosx)/cos^2x$ ,

$=1*(1-cos0)/cos^2 0$ ,

$=1*(1-1)/1^2$ ,

$=0$ .