A curve has the equation $y=\frac{\sin 2x}{2-\cos 2x}$. Show that the gradient function can be exp

Question

A curve has the equation $y=\frac{\sin 2x}{2-\cos 2x}$. Show that the gradient function can be expressed in the form $\frac{k\cos 2x-2}{(2-\cos 2x)^2}$, where $k$ is a constant.[3] Find the acute angle between the tangent to the curve at $x=\frac{\pi}{12}$ and the line $y=0$.[3]

Accepted Answer

$\text{(a) }k=4\quad\text{(b) }48.7^\circ$

2025 AISS PRELIMS P2 Q1

2025 AISS PRELIMS P2 Q1

Solution:

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