## Proof That the Absolute Value of Cot pi z is at Most 2

Theorem

forwhereis the square with vertices at

Proof

Note that withthat

(1)

Iflies on one of the vertical sides ofthensohence

Iflies on one of the horizontal sides ofthenWrite (1) as

Thenfor

Theorem

forwhereis the square with vertices at

Proof

Note that withthat

(1)

Iflies on one of the vertical sides ofthensohence

Iflies on one of the horizontal sides ofthenWrite (1) as

Thenfor