2026 NORTHBROOKS P2 Q2

2026 NORTHBROOKS P2 Q2

Secondary 4
9 marks
  1. Given that \(\tan A=3\tan B\), show that \(\tan(A-B)=\dfrac{\sin2B}{1+2\sin^2B}\).[4]
    1. Solve, in terms of \(\pi\), the equation \(\cos2x=\sqrt3\cos x-1\) for \(0\le x\le2\pi\).[4]
    2. Hence solve, in terms of \(\pi\), \(\cos x=\sqrt3\cos\dfrac{x}{2}-1\) for \(0\le x\le2\pi\).[1]

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Answer:(a) Identity shown. (b)(i) \(x=\dfrac\pi6,\dfrac\pi2,\dfrac{3\pi}2,\dfrac{11\pi}6\). (ii) \(x=\dfrac\pi3,\pi\).

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