Trigonometry/For Enthusiasts/Less-Used Trig Identities

Triangle Identities edit

In addition to the Law of Sines, the Law of Cosines, and the Law of Tangents, there are numerous other identities that apply to the three angles A, B, and C of any triangle (where A+B+C=180° and each of A, B, and C is greater than zero). Some of the most notable ones follow:

 
 
 
 
 
 
 
 

Pythagoras edit

 
 
 

These are all direct consequences of Pythagoras's theorem.

Sum/Difference of angles edit

 
 
 

Product to Sum edit

 
 
 

Sum and difference to product edit

  , where   and  
 
 
 

Multiple angle edit

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

These are all direct consequences of the sum/difference formulae

Half angle edit

 
 
 
 

In cases with   , the sign of the result must be determined from the value of   . These derive from the   formulae.

Power Reduction edit

 
 
 

Even/Odd edit

 
 
 
 
 
 

Calculus edit