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Double Angle Formula

How to use formula to express exact values

The double angle identities take two different formulas
  • sin2θ = 2sinθcosθ
  • cos2θ = cos²θ − sin²θ
    The double angle formulas can be quickly derived from the angle sum formulas
    Here's a reminder of the angle sum formulas:
  • sin(A+B) = sinAcosB + cosAsinB
  • cos(A+B) = cosAcosB − sinAsinB
    • If you let θ = A = B in the double angle identities then you get
  • A + B = 2θ
  • sin(2θ) = sinθcosθ + cosθsinθ
      • sin(2θ) = 2sinθcosθ
  • cos(2θ) = cosθcosθ − sinθsinθ
    • cos(2θ) = cos²θ − sin²θ
double angle formula | angle sum formula | pythagorean identities
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