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#.