Mixed assessment · Question 3
5 written marks
Let \(\displaystyle F(x)=\frac{1-\cos x}{\sin x}+\frac{\sin x}{1-\cos x}\), for \(0\lt x\lt 2\pi\) where defined.
Part a · 3 marks
Prove that \(\displaystyle F(x)=\frac2{\sin x}\) on its original domain and state the excluded input within the given interval.
Part b · 2 marks
Solve \(F(x)=-4\).
Complete-answer checking, worked solutions and indicative written criteria.
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