\(A\), \(B\) and \(C\) are the angles of a triangle.
Show that \(\tan C=-\tan(A+B)\).[2]
Given that angle \(A=30^\circ\) and angle \(B=45^\circ\), find \(\tan C\) in the form of \(a+\sqrt b\), where \(a\) and \(b\) are integers. You are to show your full working without the use of a calculator.[3]
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Answer:(i) Identity shown. (ii) \(-2-\sqrt3\); the printed plus-surd form is erroneous.