SUMthing...special

Algebra Level 2

$A=\ln(\tan 10^\circ) +\ln(\tan 20^\circ)+\ln(\tan 30^\circ)+...+\ln(\tan80°)$

Evaluate $A$ .

1 solution

Jim Chale
Jul 2, 2018

We observe that:

$ln(\tan 10°)+ln(\tan 80°)=ln(\tan 10° \tan 80°)=ln(\tan 10° \cot 10°)=ln(1)=0$

So we have:

$A=ln1+ln1+...+ln1=0$