Question

当X趋于零时,求解secx^2-cosx/1-cosx的答案和详细步骤,

Answer 1

∵(sec²x-cosx)/(1-cosx)

=(1/cos²x-cosx)/(1-cosx)

=(1-cos³x)/[cos²x(1-cosx)]

=(1-cosx)(1+cosx+cos²x)/[cos²x(1-cosx)]

=(1+cosx+cos²x)/cos²x

∴lim(x-->0)(sec²x-cosx)/(1-cosx)

=lim(x-->0)(1+cosx+cos²x)/cos²x

=(1+1+1)/1

=3