A zero factor is not disposable
8 written marks
Work throughout on \(0\le x\lt 2\pi\).
Part a · 3 marks
Solve \(\cos x(2\sin x+1)=0\).
Part b · 2 marks
A student divides the original equation by \(\cos x\). State exactly which solutions are lost, and explain why the division is not valid at them.
Part c · 3 marks
Instead solve \(\tan x(2\sin x+1)=0\), keeping the original tangent domain.
Complete-answer checking, worked solutions and indicative written criteria.
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