Show that
cos2xsinx+sin2xcosx≡cscx,x≠nπ2, n∈Z\frac{\cos 2x}{\sin x} + \frac{\sin 2x}{\cos x} \equiv \csc x, \quad x \neq \frac{n\pi}{2}, \; n \in \mathbb{Z}sinxcos2x+cosxsin2x≡cscx,x=2nπ,n∈Z
In a study of fluid dynamics, the pressure coefficient PPP is modeled by the equation
(cos2θsinθ+sin2θcosθ)2=7−cotθ\left( \frac{\cos 2\theta}{\sin \theta} + \frac{\sin 2\theta}{\cos \theta} \right)^2 = 7 - \cot \theta(sinθcos2θ+cosθsin2θ)2=7−cotθ
Hence solve this equation for 0<θ<π0 < \theta < \pi0<θ<π, giving your answers to 3 significant figures as appropriate.
Using the result from part (a), or otherwise, find the exact value of
∫π6π4(cos2xsinx+sin2xcosx)cotx dx\int_{\frac{\pi}{6}}^{\frac{\pi}{4}} \left( \frac{\cos 2x}{\sin x} + \frac{\sin 2x}{\cos x} \right) \cot x \, dx∫6π4π(sinxcos2x+cosxsin2x)cotxdx
Practise Edexcel A Level Maths Trigonometry and Modelling with exam-style questions for A Level Maths. 100 questions 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, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.