7.5 Proving Trigonometric Identities

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Show that

$n∈Z\frac{\cos 2x}{\sin x} + \frac{\sin 2x}{\cos x} \equiv \csc x, \quad x \neq \frac{n\pi}{2}, \; n \in \mathbb{Z}$

[3]

In a study of fluid dynamics, the pressure coefficient $P$ is modeled by the equation

$(cos⁡2θsin⁡θ+sin⁡2θcos⁡θ)2=7−cot⁡θ\left( \frac{\cos 2\theta}{\sin \theta} + \frac{\sin 2\theta}{\cos \theta} \right)^2 = 7 - \cot \theta$

Hence solve this equation for $\theta < \pi$ , giving your answers to 3 significant figures as appropriate.

[5]

Using the result from part (a), or otherwise, find the exact value of

$dx\int_{\frac{\pi}{6}}^{\frac{\pi}{4}} \left( \frac{\cos 2x}{\sin x} + \frac{\sin 2x}{\cos x} \right) \cot x \, dx$

[3]

7.5 Proving Trigonometric Identities Questions

Practise Edexcel A Level Maths 7.5 Proving Trigonometric Identities with exam-style questions for A Level Maths. 27 questions, 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.