Trigonometry/For Enthusiasts/Less-Used Trig Identities

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Triangle IdentitiesEdit

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:

 
 
 
 
 
 
 
 

PythagorasEdit

 
 
 

These are all direct consequences of Pythagoras's theorem.

Sum/Difference of anglesEdit

 
 
 

Product to SumEdit

 
 
 

Sum and difference to productEdit

  , where   and  
 
 
 

Multiple angleEdit

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

These are all direct consequences of the sum/difference formulae

Half angleEdit

 
 
 
 

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

Power ReductionEdit

 
 
 

Even/OddEdit

 
 
 
 
 
 

CalculusEdit