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Further trigonometric identitiesEdexcel International A Level Maths: Flashcards

What these 12 flashcards ask

  • Identity linking \sec^2\theta and \tan^2\theta?
  • Identity linking \operatorname{cosec}^2\theta and \cot^2\theta?
  • How do you derive \sec^2\theta=1+\tan^2\theta?
  • How do you derive \operatorname{cosec}^2\theta=1+\cot^2\theta?
  • Rearrange: \tan^2\theta=?
  • Rearrange: \cot^2\theta=?
  • If \tan\theta=\frac{5}{12} (\theta acute), find \sec\theta.
  • What is \sec^2\theta-\tan^2\theta?
  • What is \operatorname{cosec}^2\theta-\cot^2\theta?
  • What is the difference between an identity and an equation?
  • Strategy for proving an identity?
  • Simplify \dfrac{\sec^2x-1}{\sec^2x}.

Exam questions on Further trigonometric identities

  1. The angle θ\theta is acute and tan⁡θ=512\tan\theta=\frac{5}{12}.
    Find the exact value of sec⁡θ−tan⁡θ\sec\theta-\tan\theta.2 marks
  2. Throughout, xx is any angle for which the expressions are defined.
    Show that sec⁡2x−1sec⁡2x≡sin⁡2x\dfrac{\sec^2x-1}{\sec^2x}\equiv\sin^2x.2 marks
  3. Angles are measured in degrees and 0≤θ<3600\le\theta<360.
    Given that sec⁡2θ=4tan⁡θ−2\sec^2\theta=4\tan\theta-2, find the two possible values of tan⁡θ\tan\theta.3 marks
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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).