2025 JVSS PRELIMS P1 Q3

2025 JVSS PRELIMS P1 Q3

Secondary 4
10 marks
2025 Jurongville Secondary School Prelims A Math Paper 1
  1. Prove that \(\dfrac{\cot^2 \theta - \tan^2 \theta}{(1 + \tan^2 \theta)(1 + \cot^2 \theta)} = \cos 2\theta\).[5]
  2. Hence, solve the equation \(\dfrac{(\cot^2 \theta - \tan^2 \theta)(2\sin 2\theta)}{(1 + \tan^2 \theta)(1 + \cot^2 \theta)} = 0.75\) for \(-90^\circ \leq \theta \leq 90^\circ\).[5]

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Answer:(a) \(\dfrac{\cot^2\theta-\tan^2\theta}{(1+\tan^2\theta)(1+\cot^2\theta)}=\cos2\theta\). (b) \(\theta=-77.9^\circ,\ -57.1^\circ,\ 12.1^\circ,\ 32.9^\circ\).

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