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1 Pure Mathematics

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Question 661
i.

Show that

cot⁡θ−tan⁡θcot⁡θ+tan⁡θ≡cos⁡2θ \frac{\cot \theta - \tan \theta}{\cot \theta + \tan \theta} \equiv \cos 2\theta cotθ+tanθcotθ−tanθ​≡cos2θ

for θ≠nπ2\theta \neq \frac{n\pi}{2}θ=2nπ​ where n∈Zn \in \mathbb{Z}n∈Z.

[3]
ii.

The power output PPP (in Watts) of a specific AC circuit component is modelled by the function P(t)=11cos⁡2(2t−40∘)P(t) = 11 \cos^2(2t - 40^\circ)P(t)=11cos2(2t−40∘), where ttt is a phase angle measured in degrees and 0∘≤t<90∘0^\circ \le t < 90^\circ0∘≤t<90∘.

Determine the values of ttt for which the power output is exactly 333 Watts, giving your answers to one decimal place. (Solutions based entirely on graphical or numerical methods are not acceptable.)

[5]
Markscheme

1 Pure Mathematics Questions

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