Pythagorean Identity

The Pythagorean Theorem

x2 + y2  = r2 

Divide both sides by r2,

x2     y2      r2  
r2       r2      r2  

or 
  x  2     y  2       
r         r         

where the terms on the left are the definitions of cosine and sine, respectively.  Thus,

cos2q + sin2q = 1