A missing point changes an equation
8 written marks
Define \(\displaystyle H(x)=\frac{\cos^2x}{1-\sin x}\) for \(0\le x\lt 2\pi\), wherever the quotient exists.
Part a · 2 marks
Find the excluded input and simplify \(H(x)\) on its original domain.
Part b · 3 marks
Solve \(\displaystyle H(x)=\frac12\).
Part c · 3 marks
Decide whether \(H(x)=2\) has a solution, and explain the difference from solving \(1+\sin x=2\) on the whole interval.
Complete-answer checking, worked solutions and indicative written criteria.
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