Sum of logarithms: ln(tan(1°)) + ln(tan(2°)) + ... + ln(tan(89°)) = ?

[Noismaker]

Sum of logarithms: ln(tan(1°)) + ln(tan(2°)) + ... + ln(tan(89°)) = ?

ln(tan(1°))+ln(tan(2°))+...ln(tan(89°))= ?

ty

 

[tkhunny]

That's a lovely problem. What are your thoughts?

You MAY wish to transform a few things. These rules come immediately to mind:

tan(x) = sin(x)/cos(x)

log(x/y) = log(x) - log(y)

sin(x) = cos(90deg - x)

cos(x) = sin(90deg - x)

Or, maybe that's all a wild goose chase. Let's see your efforts.