2025 Bedok View Secondary School Prelims A Math Paper 1
Explain why the principal value of \(\cos^{-1}\left(-\frac{\sqrt{2}}{2}\right)\) cannot be \(-\frac{\pi}{4}\).[1]
Prove that \(\cot A+\tan A=\sec A\cosec A\).[4]
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Answer:(a) \(-\frac{\pi}{4} otin[0,\pi]\), so it cannot be the principal value of \(\cos^{-1}\left(-\frac{\sqrt{2}}{2}\right)\). (b) \(\cot A+\tan A=\frac{\cos A}{\sin A}+\frac{\sin A}{\cos A}=\frac{\cos^2A+\sin^2A}{\sin A\cos A}=\frac{1}{\sin A\cos A}=\sec A\cosec A\).