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1.8 E: Trigonometry

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Question 12

Prove the following identities for all valid values of AAA.

a.

sec⁡2A+cosec⁡2A≡tan⁡2A+cot⁡2A+2\sec^2 A + \operatorname{cosec}^2 A \equiv \tan^2 A + \cot^2 A + 2sec2A+cosec2A≡tan2A+cot2A+2

[2]
b.

(tan⁡A+cot⁡A)2≡sec⁡2A+cosec⁡2A(\tan A + \cot A)^2 \equiv \sec^2 A + \operatorname{cosec}^2 A(tanA+cotA)2≡sec2A+cosec2A

[3]
Markscheme

1.8 E: Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.8 E: Trigonometry

317 exam-style questions on AQA A Level Maths 1.8 E: Trigonometry, covering 1.8.1 Trigonometric definitions, rules and radians, 1.8.2 Small angle approximations (A-level only), 1.8.3 Trigonometric functions and exact values, 1.8.4 Reciprocal and inverse trigonometric functions (A-level only), 1.8.5 Trigonometric identities, 1.8.6 Compound and double angle formulae (A-level only), 1.8.7 Solving trigonometric equations, 1.8.8 Proofs with trigonometric identities, and 1.8.9 Trigonometry in context. Each one has a worked solution and a mark scheme showing where the marks go.

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