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1.8 E: Trigonometry

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Question 78

Prove the following identities.

a.

sec⁡2x−cosec⁡2x≡tan⁡2x−cot⁡2x\sec^2 x - \operatorname{cosec}^2 x \equiv \tan^2 x - \cot^2 xsec2x−cosec2x≡tan2x−cot2x

[2]
b.

(sec⁡x−cos⁡x)2≡tan⁡2x−sin⁡2x(\sec x - \cos x)^2 \equiv \tan^2 x - \sin^2 x(secx−cosx)2≡tan2x−sin2x

[4]
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.

Question bank