Prove the following trigonometric identities:
cosec2θ−sec2θ≡cot2θ−tan2θ\text{cosec}^2\theta - \sec^2\theta \equiv \cot^2\theta - \tan^2\thetacosec2θ−sec2θ≡cot2θ−tan2θ
(cosecθ−sinθ)2≡cot2θ−cos2θ(\text{cosec}\theta - \sin\theta)^2 \equiv \cot^2\theta - \cos^2\theta(cosecθ−sinθ)2≡cot2θ−cos2θ
Practise AQA A Level Maths 1.8 E: Trigonometry with exam-style questions for A Level Maths. 239 questions 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, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
