If A, B and C are the angles of a triangle, then cotA·cotB + cotB·cotC + cotC·cotA equals:

Since $A+B=180$° − $C$, cot$(A+B)=-$cotC. Using cot$(A+B)=$ (cotA·cotB − 1)/(cotA + cotB), we get cotA·cotB − 1 = −cotC(cotA + cotB), which rearranges to cotA·cotB + cotB·cotC + cotC·cotA = 1. Check with $A=30$°, $B=60$°, $C=90$°: cot90° = 0, so the sum is just $1.732\times 0.577=1$.