A-Level Maths OCR B (MEI) (H640)

#7.19 Double angle formulae

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Know and use identities for sin⁡2θ\sin{2θ}, cos⁡2θ\cos{2θ}, tan⁡2θ\tan{2θ}.

Includes understanding derivations from sin⁡(θ±ϕ)\sin{(θ \pm ϕ)}, cos⁡(θ±ϕ)\cos{(θ \pm ϕ)}, tan⁡(θ±ϕ)\tan{(θ \pm ϕ)}.

  • cos⁡2θ≡cos⁡2θ−sin⁡2θ\cos{2θ} ≡ \cos^2{θ} - \sin^2{θ}
  • cos⁡2θ≡2cos⁡2θ−1\cos{2θ} ≡ 2\cos^2{θ} - 1
  • cos⁡2θ≡1−2sin⁡2θ\cos{2θ} ≡ 1 - 2\sin^2{θ}

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