SOLUTION: What is sin(arctan root3) + cos(arccot root3)?

Question 669562: What is sin(arctan root3) + cos(arccot root3)?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
DISCLAIMER:
There is probably a cuter way to prove it,
invoking trigonometric identities and starting with
<---> and
<--->.
However, my head hurts trying to think of it,
so I will go the way that is more natural to me.

The inverse trigonometric functions and are defined in a manner that makes sense.
We know that

and

There are infinite other angles with ,
but or
because it is defined as the angle between and (or between and )
That has for cotangent.
So

We also know that

and

and or
because is defined with with a range of to ( to ).
So

In sum
Cute!
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