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1 Pure Mathematics

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Question 187
a.

Prove that

cosec⁡θcosec⁡θ−sin⁡θ≡sec⁡2θ\displaystyle \frac{\operatorname{cosec}\theta}{\operatorname{cosec}\theta - \sin\theta} \equiv \sec^2\thetacosecθ−sinθcosecθ​≡sec2θ

[4]
b.

Hence solve, for 0<θ<2π0 < \theta < 2\pi0<θ<2π, the equation

cosec⁡θcosec⁡θ−sin⁡θ=2tan⁡θ\displaystyle \frac{\operatorname{cosec}\theta}{\operatorname{cosec}\theta - \sin\theta} = 2\tan\thetacosecθ−sinθcosecθ​=2tanθ

Give your answers in terms of π\piπ.

[3]
Markscheme

1 Pure Mathematics Questions

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