Addition and Double Angle Formulas

Addition and Double Angle Formulas

• Sin(A+B) and Sin(A-B) formulas:

  • The sine of the sum of two angles A and B can be represented as Sin(A+B) = SinA CosB + CosA SinB.
  • The sine of the difference between two angles A and B is represented by Sin(A-B) = SinA CosB – CosA SinB.

• Cos(A+B) and Cos(A-B) formulas:

  • Cos(A+B) = CosA CosB - SinA SinB represents the cosine of the sum of two angles.
  • The cosine of the difference between two angles A and B is Cos(A-B) = CosA CosB + SinA SinB.

• Tan(A+B) and Tan(A-B) formulas:

  • The tangent of the sum of two angles A and B can be found using Tan(A+B) = (TanA + TanB) / (1 - TanA TanB).
  • The tangent of the difference between two angles A and B is Tan(A-B) = (TanA – TanB) / (1 + TanA TanB).

• Double angle formulas:

  • Sin2A = 2SinA CosA.
  • Cos2A can take a few representations: Cos²A - Sin²A, 2Cos²A - 1, or 1 - 2Sin²A. Choose whichever is most useful in the context of the problem you’re working on.
  • The double angle formula for tangent is Tan2A = 2TanA / (1 – Tan²A)

Strategically applying these formulas can simplify the process of solving more complex trigonometric problems.