Use the identity cos2θ+sin2θ=1\cos^2\theta + \sin^2\theta = 1cos2θ+sin2θ=1 to prove that cosec2θ=1+cot2θ\text{cosec}^2\theta = 1 + \cot^2\thetacosec2θ=1+cot2θ.
Solve, for 0≤θ≤2π0 \leq \theta \leq 2\pi0≤θ≤2π, the equation,
cosec2θ+cot2θ=7 \text{cosec}^2\theta + \cot^2\theta = 7 cosec2θ+cot2θ=7Give your answers in terms of π\piπ.
54 exam-style questions on Edexcel A Level Maths Trigonometric Functions, covering 6.1 Secant, Cosecant and Cotangent, 6.2 Graphs of Sec x, Cosec x and Cot x, 6.3 Using Sec x, Cosec x and Cot x, 6.4 Trigonometric Identities, and 6.5 Inverse Trigonometric Functions. Each one has a worked solution and a mark scheme showing where the marks go.