Question

Lim x tends to pi/2 tan^2x - 2tanx - 3 /tan^2x - 4tanx +3

Answer 1

Limit x->pi/2(tan^2x-2tanx-3)/(tan^2x-2tanx+3)

=Limit x->pi/2(tan^2x-3tanx+tanx-3)/(tan^2x-3tanx-tanx+3)

= Limit x->pi/2(tanx+1)/(tanx-1)

=Limit x->pi/2(sinx +cosx)/(sinx-cosx)

Put the limits

=(sin90+cos90)/(sin90-cos90)

=(1+0)/(1-0)

=1/1

=1