An identity gives a shorter solving route
8 written marks
Consider \(\displaystyle F(x)=\frac{\sin x}{1+\cos x}+\frac{1+\cos x}{\sin x}\) for \(0\le x\le2\pi\).
Part a · 2 marks
List every input excluded from the original expression.
Part b · 3 marks
Prove that \(\displaystyle F(x)=\frac2{\sin x}\) on its domain.
Part c · 3 marks
Solve \(F(x)=4\).
Complete-answer checking, worked solutions and indicative written criteria.
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