Prove that:
cosec4θ−cot4θ≡1+2cot2θ\text{cosec}^4 \theta - \cot^4 \theta \equiv 1 + 2\cot^2 \thetacosec4θ−cot4θ≡1+2cot2θ
Hence solve, for 0≤θ≤3600 \leq \theta \leq 3600≤θ≤360, the equation,
cosec4θ−cot4θ=7 \text{cosec}^4 \theta - \cot^4 \theta = 7 cosec4θ−cot4θ=7317 exam-style questions on OCR A Level Maths 1.5 Trigonometry, covering 1.5.1 Definitions for all arguments, 1.5.2 Sine and cosine rules, 1.5.3 Area of a triangle, 1.5.4 Radian measure (A-level only), 1.5.5 Small angle approximations (A-level only), 1.5.6 Graphs of basic trigonometric functions, 1.5.7 Exact values in radians (A-level only), 1.5.8 Reciprocal and inverse trigonometric ratios (A-level only), 1.5.9 Graphs of reciprocal and inverse functions (A-level only), 1.5.10 Trigonometric identities, 1.5.11 Further trigonometric identities (A-level only), 1.5.12 Double angle and compound angle formulae (A-level only), 1.5.13 Geometrical proofs of formulae (A-level only), 1.5.14 Harmonic form Rcos / Rsin (A-level only), 1.5.15 Trigonometric equations, 1.5.16 Proof involving trigonometric functions (A-level only), and 1.5.17 Trigonometric functions in context. Each one has a worked solution and a mark scheme showing where the marks go.