Prove that 11+cosθ+11−cosθ≡2sin2θ\dfrac{1}{1 + \cos\theta} + \dfrac{1}{1 - \cos\theta} \equiv \dfrac{2}{\sin^2\theta}1+cosθ1+1−cosθ1≡sin2θ2 where sinθ≠0\sin\theta \neq 0sinθ=0.
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.