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Compound angle formulas

Compound angle formulas are a set of trigonometric identities for writing trigonometric ratios of a sum of two or more angles as trigonometric ratios of each of the constituent angles.

A compound angle is the sum of two or more angles. For example, if there are two angles measuring A and B respectively then A + B is a compound angle. A compound angle can have more than two angles for its sum.

Compound angle formulas are a set of trigonometric identities which help in converting a trigonometric function of a compound angle (for example sin(A + B)) into an expression consisting of trigonometric functions of only the constituent angles (viz sin(A) and sin(B).

Compound angle formulas for a sum of two angles

  • `cos(A + B) = cos(A) cos(B) - sin(A) sin(B)`
  • `cos(A - B) = cos(A) cos(B) + sin(A) sin(B)`
  • `sin(A + B) = sin(A) cos(B) + cos(A) sin(B)`
  • `sin(A - B) = sin(A) cos(B) - cos(A) sin(B)`
  • `tan(A + B) = (tan(A) + tan(B))/(1 - tan(A) tan(B))`
  • `tan(A - B) = (tan(A) - tan(B))/(1 + tan(A) tan(B))`

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