Exact cotangent of an angle from an equation between a shifted cosine and a shifted sine

IB Year 6 | Grade 12

4 marks

The angle \(x\) satisfies \(2\cos(x+60^\circ)=\sin(x+45^\circ)\). Determine \(\cot x\) exactly, simplifying your answer.[4]

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Answer:\(\cot x=1+\sqrt2+2\sqrt3+\sqrt6\)

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