7.5 Proving Trigonometric Identities

List view

Given that $sin⁡θ≠±1\sin \theta \neq \pm 1$ , prove the identity $11−sin⁡θ+11+sin⁡θ≡2sec⁡2θ\frac{1}{1 - \sin \theta} + \frac{1}{1 + \sin \theta} \equiv 2 \sec^2 \theta$

[3]

Hence, find the set of values of $k$ for which the equation $11−sin⁡θ+11+sin⁡θ=k\frac{1}{1 - \sin \theta} + \frac{1}{1 + \sin \theta} = k$ has real solutions. Fully justify your answer.

[3]

Given that $θ\theta$ is in the second quadrant (reflex angle between $90∘90^\circ$ and $180∘180^\circ$ ) and $11−sin⁡θ+11+sin⁡θ=10\frac{1}{1 - \sin \theta} + \frac{1}{1 + \sin \theta} = 10$ find the exact value of $tan⁡θ\tan \theta$ .

[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.