Formulas

Algebraic Identities
Trigonometric Identities

Algebraic Identities

(a ± b)2 = a2 ± 2 · a · b + b2

(a + b) · (a − b) = a2 − b2

(a ± b)3 = a3 ± 3 · a2 · b + 3 · a · b2 ± b3

(a + b + c)2 = a2 + b2 + c2 + 2 · a · b + 2 · a · c + 2 · b · c

a3 + b3 = (a + b) · (a2 − ab + b2)

a3 − b3 = (a − b) · (a2 + ab + b2)

(x + a) (x + b) = x2 + (a + b) x + ab

 

 

Trigonometric Identities

Pythagorean Identities

 

sin2 θ + cos2 θ = 1

tan2 θ + 1 = sec2 θ

cot2 θ + 1 = csc2 θ

Reciprocal Identities
Ratio Identities
Cofunction Identities, radians Cofunction Identities, degrees
sin (90° – x) = cos x cos (90° – x) = sin x
tan (90° – x) = cot x cot (90° – x) = tan x
sec (90° – x) = csc x csc (90° – x) = sec x

 

Periodicity Identities, radians Periodicity Identities, degrees
sin (x + 2π) = sin x csc (x + 2π) = csc x sin (x + 360°) = sin x csc (x + 360°) = csc x
cos (x + 2π) = cos x sec (x + 2π) = sec x cos (x + 360°) = cos x sec (x + 360°) = sec x
tan (x + π) = tan x cot (x + π) = cot x tan (x + 180°) = tan x sin (x + 180°) = cot x

Sum/Difference Identities

Double Angle Identities

 

Half Angle Identities
  or  

  or  

 

  or    or  

 

Product to Sum Identities

Sum to Product Identities

 

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