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2023 SCSS P2 Q8
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2023 SCSS P2 Q8
Secondary 4
11 marks
Prove that \(\dfrac{\cot^2\theta-1}{\operatorname{cosec}^2\theta}=\cos2\theta\).
[3]
Write \(5\cos x-2\sin x\) in the form \(R\cos(x+\alpha)\), where \(R>0\) and \(0^\circ<\alpha<90^\circ\).
[4]
Hence, or otherwise, find the least value of \(8+5\cos x-2\sin x\) and the smallest positive value of \(x\) for which this occurs.
[4]
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Answer:
(a) Proved. (b)(i) \(\sqrt{29}\cos(x+21.8^\circ)\) (rounded angle). (ii) \(8-\sqrt{29}\); \(x=158.2^\circ\).
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