A-Level Maths Edexcel (9MA0)

#1.5.5 Pythagorean identities

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Understand and use

  • tan⁡θ=sin⁡θcos⁡θ\tan{θ} = \dfrac{\sin{θ}}{\cos{θ}}
  • sin⁡2θ+cos⁡2θ=1\sin^2{θ} + \cos^2{θ} = 1
  • sec⁡2θ=1+tan⁡2θ\sec^2{θ} = 1 + \tan^2{θ} and
  • cosec⁡2θ=1+cot⁡2θ\cosec^2{θ} = 1 + \cot^2{θ}

These identities may be used to solve trigonometric equations and angles may be in degrees or radians. They may also be used to prove further identities.