The diagram above shows a right-angled triangle $ABC$, where $AB=\sqrt{2}$ cm, and \(BC=\sq

Question

The diagram above shows a right-angled triangle $ABC$, where $AB=\sqrt{2}$ cm, and $BC=\sqrt{2}+\sqrt{3}$ cm. Find the exact value of $\tan \angle ACB$ in the form of $a+\sqrt{b}$, where $a$ and $b$ are integers.[2] Hence, find the exact value of $\sec^2 \angle ACB$ in the form $m+n\sqrt{k}$, where $m$ and $n$ are integers.[2]

Accepted Answer

(a) $\tan \angle ACB=\sqrt{6}-2$ (b) $\sec^2 \angle ACB=11-4\sqrt{6}$

(A Math) 2025 CCHY PRELIMS P1 Q1

(A Math) 2025 CCHY PRELIMS P1 Q1

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