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1 Pure Mathematics

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Question 127
a.

Prove that

sin⁡θcos⁡θ+cos⁡θsin⁡θ≡2cosec⁡2θ\displaystyle \frac{\sin\theta}{\cos\theta} + \frac{\cos\theta}{\sin\theta} \equiv 2\operatorname{cosec}2\thetacosθsinθ​+sinθcosθ​≡2cosec2θ

[3]
b.

Hence solve, for 0°≤θ<360°0° \leq \theta < 360°0°≤θ<360°, the equation

sin⁡θcos⁡θ+cos⁡θsin⁡θ=5\displaystyle \frac{\sin\theta}{\cos\theta} + \frac{\cos\theta}{\sin\theta} = 5cosθsinθ​+sinθcosθ​=5

Give your answers to one decimal place.

[4]
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1 Pure Mathematics Questions

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