Angle Difference Formula

How to use formula to express exact values

The angle difference identities take two different formulas
  • sin(A − B) = sinAcosB − cosAsinB
  • cos(A − B) = cosAcosB + sinAsinB

These formulas allow you to express the exact value of trigonometric expressions that you could not otherwise express. Consider the cos(15°). Unlike the cos(60°) which can be expressed as ½, the cos(15°) cannot simply be represented as a rational expression. However, the angle difference formula allows you to represent the exact value of this function

Picture of angle difference formula

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