2025 CGS PRELIMS P2 Q3

2025 CGS PRELIMS P2 Q3

Secondary 4
8 marks
2025 Crescent Girls' School Prelims A Math Paper 2
  1. Show that \(\frac{d}{dx}\left(\tan^3 2x\right)=6\sec^4 2x-6\sec^2 2x\).[3]
  2. Hence, find the exact value of \(\int_0^{\frac{\pi}{8}} \sec^4 2x\, dx\).[5]

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Answer:(a) \(\frac{d}{dx}(\tan^3 2x)=6\sec^4 2x-6\sec^2 2x\) (b) \(\displaystyle \int_0^{\frac{\pi}{8}}\sec^4 2x\,dx=\frac{2}{3}\)

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