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

Question

$A$, $B$ and $C$ are the angles of a triangle. Given that $\sin(A + B) = \frac{12}{13}$. Find the exact value of $\tan C$ . Show your working clearly.[3] Evaluate $\cos\left[(A + B) + \frac{\pi}{3}\right]$ . Leave your answer in surd form.[3]

Accepted 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.

2024 GESS PRELIMS P2 Q4

2024 GESS PRELIMS P2 Q4

Solution:

Solution locked