(i)[2]
Differentiate $\frac{\cos x}{\sin x}$ to demonstrate that, when $y = \cot x$, $\frac{dy}{dx} = -\cosec^2 x$.
(ii)[6]
Show by calculation that $\int_{\frac{\pi}{4}}^{\frac{3\pi}{4}} x\,\cosec^2 x\,dx = \frac{1}{4}(\pi + \ln 4)$.
Mathematics 9709 · AS & A Level · Integration