Prove that
2cosec2θ=sinθcosθ+cosθsinθ 2 \operatorname{cosec} 2\theta = \frac{\sin \theta}{\cos \theta} + \frac{\cos \theta}{\sin \theta} 2cosec2θ=cosθsinθ+sinθcosθSketch the graph of y=2cosec2θy = 2 \operatorname{cosec} 2\thetay=2cosec2θ for 0∘<θ<360∘0^\circ < \theta < 360^\circ0∘<θ<360∘.
Given that θ=15∘\theta=15^\circθ=15∘ is a solution of
sinθcosθ+cosθsinθ=k \frac{\sin \theta}{\cos \theta} + \frac{\cos \theta}{\sin \theta} = k cosθsinθ+sinθcosθ=kfind the value of k k\,k and the other solutions for 0≤θ<360∘0 \leq \theta < 360^\circ0≤θ<360∘, giving your answers to 1 decimal place.
348 exam-style questions on Edexcel A Level Maths Trigonometry and Modelling, covering 7.1 Addition Formulae, 7.2 Double Angle Formulae, 7.3 Solving Trigonometric Equations, 7.4 Simplifying a cos x +- b sin x, 7.5 Proving Trigonometric Identities, and 7.6 Modelling with Trigonometric Functions. Each one has a worked solution and a mark scheme showing where the marks go.