2025 MGS PRELIMS P2 Q9
2025 MGS PRELIMS P2 Q9
Secondary 4
9 marks
- Prove that \( \cot x + \frac{\sin x}{1+\cos x}=\cosec x \).[3]
- Hence solve \( \cot x + \frac{\sin x}{1+\cos x}=4\cos x \), for \( 0\le x\le 2\pi \).[4]
- Using the result in part (a), find the set of values of the \( k \), such that the equation \[ \cot x + \frac{\sin x}{1+\cos x}=\frac{1}{k},\ k\ne 0 \] has solutions.[2]
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Answer:(a) \(\cot x+\dfrac{\sin x}{1+\cos x}=\cosec x\) (b) \(x=\dfrac\pi{12},\dfrac{5\pi}{12},\dfrac{13\pi}{12},\dfrac{17\pi}{12}\) (c) \(-1\leq k<0\) or \(0<k\leq1\)
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