Mathwords logoReference LibraryMathwords

Sum to Product Identities

Sum to Product Identities

Trig identities which show how to rewrite sums and differences of sines or cosines as products.

 

Sum to Product Identities

sin x + sin y = 2 sin((x+y)/2) cos((x-y)/2)

sin x minus sin y equals 2 cos((x+y)/2) times sin((x-y)/2)

cos x + cos y = 2cos((x+y)/2)cos((x-y)/2)

cos x minus cos y equals negative 2 times sin((x+y)/2) times sin((x-y)/2)

 

See also

Product to sum identities