Prove that cscθcscθ−sinθ≡sec2θ\displaystyle \frac{\csc \theta}{\csc \theta - \sin \theta} \equiv \sec^2 \thetacscθ−sinθcscθ≡sec2θ
Hence solve, for 0<θ<2π0 < \theta < 2\pi0<θ<2π, cscθcscθ−sinθ=2tanθ\displaystyle \frac{\csc \theta}{\csc \theta - \sin \theta} = 2 \tan \thetacscθ−sinθcscθ=2tanθ
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.