Show that $\frac{\mathrm{d}}{\mathrm{d}x}(\cot x) = -\mathrm{cosec}^2 x$.[2] A curve has equa

Question

Show that $\frac{\mathrm{d}}{\mathrm{d}x}(\cot x) = -\mathrm{cosec}^2 x$.[2] A curve has equation $y = \mathrm{e}^{-ax} \cot x$, where $a$ is a positive constant. There is exactly one point in the interval $-\frac{1}{2}\pi < x < 0$ at which the tangent is parallel to the $x$-axis. Find the value of $a$ and state the exact $x$-coordinate of this point.[5]

Accepted Answer

(a) $\dfrac{d}{dx}(\cot x)=-\cosec^2x$ (b) $a=2$, $x=-\dfrac{\pi}{4}$

(A Math) 2025 CCHY PRELIMS P2 Q3

(A Math) 2025 CCHY PRELIMS P2 Q3

Solution:

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