Show that \(\dfrac{\mathrm{d}}{\mathrm{d}x}\left(\dfrac{\sin3x}{1-\cos3x}\right)=-\dfrac{3}{1-\

Question

Show that $\dfrac{\mathrm{d}}{\mathrm{d}x}\left(\dfrac{\sin3x}{1-\cos3x}\right)=-\dfrac{3}{1-\cos3x}$.[3] Hence evaluate the exact value of $\displaystyle\int_{\pi/12}^{\pi/6}\dfrac{1}{1-\cos3x}\,\mathrm{d}x$.[3]

Accepted Answer

$\dfrac{\sqrt2}{3}$

Sine quotient with a triple angle

Sine quotient with a triple angle

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