A-level · Trigonometry

Proving trigonometric identitiesExam-style questions

A reliable method for proving trig identities, drawing on the whole toolkit — Pythagorean, reciprocal, addition and double-angle identities — with the common tactics (one side at a time, convert to sin/cos, combine fractions, factorise).

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20 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 2Level 3Level 4Level 5
  1. 1
    Prove that

    tan⁡θ+cot⁡θcosec⁡θ≡sec⁡θθ≠nπ2, n∈Z\frac{\tan\theta + \cot\theta}{\operatorname{cosec}\theta} \equiv \sec\theta \qquad \theta \neq \frac{n\pi}{2},\ n \in \mathbb{Z}

    (3 marks)
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