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2024 GESS PRELIMS P2 Q4

2024 GESS PRELIMS P2 Q4

6 marks

\(A\), \(B\) and \(C\) are the angles of a triangle. Given that \(\sin(A + B) = \frac{12}{13}\).

  1. Find the exact value of \(\tan C\) . Show your working clearly.[3]
  2. Evaluate \(\cos\left[(A + B) + \frac{\pi}{3}\right]\) . Leave your answer in surd form.[3]

Solution:

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Answer:Acute \(C\): (a) \(12/5\) (b) \((-5-12\sqrt3)/26\). Obtuse \(C\): (a) \(-12/5\) (b) \((5-12\sqrt3)/26\). Both are allowed by the stated givens.

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