2025 AISS PRELIMS P2 Q5

2025 AISS PRELIMS P2 Q5

Secondary 4
8 marks
2025 Ahmad Ibrahim Secondary School Prelims A Math Paper 2
  1. Prove the identity \(\dfrac{(\sin A-\cos A)(1+\sin A\cos A)}{\cos^3 A}=\tan^3 A-1\).[4]
  2. Hence solve \((\sin A-\cos A)(1+\sin A\cos A)+2\cos^3 A=0\) exactly, for \(-\pi\leq A\leq \pi\) radians.[4]

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Answer:\(\text{(a)}\hspace{0.5em}\dfrac{(\sin A-\cos A)(1+\sin A\cos A)}{\cos^3 A}=\tan^3 A-1\) \(\text{(b)}\hspace{0.5em}A=-\dfrac{\pi}{4},\ \dfrac{3\pi}{4}\)

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