2025 IGCSE Additional Mathematics February/March 0606/22 Q8

2025 IGCSE Additional Mathematics February/March 0606/22 Q8

7 marks
  1. Show that \(\dfrac{\sin\theta\tan^2\theta}{1+\tan^2\theta}\) can be written as \(\sin^3\theta\).[2]
  2. Hence solve the equation \(\dfrac{\sin3x\tan^2 3x}{1+\tan^2 3x}=\dfrac18\) for \(-180^\circ\le x\le180^\circ\).[5]

Solution:

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Answer:(a) \(\sin^3\theta\) (shown) (b) \(x=-110^\circ,-70^\circ,10^\circ,50^\circ,130^\circ,170^\circ\)

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