Landau’s beautiful proofs:

1= cos 0 = cos (x-x)

Opening cos (x-x):

1 = cos x.cos (-x) – sin x.sin (-x)

=>** 1= cos² x + sin² x**

[QED]

Let cos x= b/c, sin x = a/c

1= (b/c)² + (a/c)²

c² = b² + a²

=> Pythagoras Theorem

[QED]

Landau (1877-1938) was the successor of Minkowski at the Gottingen University (Math) before WW II.