show that cot inverse (1) + cot inverse (2) + cot inverse (3) = pi/4 ?

Question

anonymous · Answer

I believe this is not actually true...

anonymous · Answer

http://www.wolframalpha.com/input/?i=%28inverse+cotangent+of+1%29+%2B+%28inverse+cotangent+of+2%29+%2B+%28inverse+cotangent+of+3%29

anonymous · Answer

cotangent is the ratio of cosine to sine for an angle.

Inverse cotangent means that for a specific ratio, the output will be the angle that has that ratio.

$cot^{-1}(1)$ will give us the angle for which cosine is equal to sine. This turns out to be pi/4

Add in $cot^{-1}(2)$ and $cot^{-1}(3)$ and clearly the angle won't be pi/4 anymore.

anonymous · Answer

arccot(x) = arctan(1/x) if x>0

so arctan(1) = arccot(1) = pi/4
the rest are positive so it cant be true
arccot(2) = arctan(1/2) > 0
arccot(3) = arctan(1/3) > 0

anonymous · Answer

yes looks like we wrote the same thing lol

anonymous · Answer

Correct =)

anonymous · Answer

This problem was almost certainly meant to say
= pi/2