2026 IGCSE Additional Mathematics February/March 0606/22 Q9

2026 IGCSE Additional Mathematics February/March 0606/22 Q9

12 marks
  1. Show that \(\tan\theta+\cot\theta+2\sec\theta\) can be written as \(\dfrac{1+2\sin\theta}{\sin\theta\cos\theta}\).[3]
  2. Hence solve the equation \(\tan2x+\cot2x+2\sec2x=0\) for \(-180^\circ\le x\le180^\circ\).[4]
  3. Solve the equation \(3\sec(x-1)-1=\tan^2(x-1)\) where \(x\) is in radians and \(-1<x<3\).[5]

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Answer:(a) Shown. (b) \(x=-75^\circ,-15^\circ,105^\circ,165^\circ\) (c) \(x=-0.231,2.23\)

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