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