A-level · Trigonometry

The sec/cosec/cot identitiesExam-style questions

The two new Pythagorean identities 1 + tan²θ ≡ sec²θ and 1 + cot²θ ≡ cosec²θ — deriving them from sin²+cos²≡1, and using them to prove identities, simplify expressions and turn equations into a solvable quadratic.

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

DifficultyAllLevel 2Level 3Level 4Level 5
  1. 1
    Write sec⁡2θ\sec^2\theta in terms of tan⁡2θ\tan^2\theta, and cosec⁡2θ\operatorname{cosec}^2\theta in terms of cot⁡2θ\cot^2\theta.
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