2024 IGCSE Additional Mathematics May/June 0606/22 Q6

2024 IGCSE Additional Mathematics May/June 0606/22 Q6

8 marks
  1. Show that \(\sin^3x\left(\dfrac{\operatorname{cosec}x}{\cot x}\right)\) can be written as \(\sin^2x\tan x\).[3]
  2. Solve the equation \(\cos^2x\tan x-\dfrac12\tan x=0\) for \(-\pi<x<\pi\).[5]

Solution:

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Answer:(a) \(\sin^2x\tan x\), as shown. (b) \(x=-\dfrac{3\pi}4,-\dfrac\pi4,0,\dfrac\pi4,\dfrac{3\pi}4\).

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