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2026 RVHS P1 Q5

2026 RVHS P1 Q5

Junior College 2
7 marks
  1. By writing \(\cos3x\) as \(\cos(x+2x)\) and applying addition formula, show that \[\cos3x=\cos x(4\cos^2x-3).\][2]
  2. By using integration by parts, or otherwise, find \(\displaystyle\int\tan x\sin3x\,\mathrm{d}x\).[5]

Solution:

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Answer:(a) Shown (b) \(-\frac13\tan x\cos3x+\frac43\sin x-\ln|\sec x+\tan x|+C\)

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