Show that \(\dfrac{\mathrm{d}}{\mathrm{d}x}\left(\dfrac{\sin2x}{1+\cos2x}\right)=\dfrac{2}{1+\c

Question

Show that $\dfrac{\mathrm{d}}{\mathrm{d}x}\left(\dfrac{\sin2x}{1+\cos2x}\right)=\dfrac{2}{1+\cos2x}$.[3] Hence evaluate the exact value of $\displaystyle\int_0^{\pi/6}\dfrac{1}{1+\cos2x}\,\mathrm{d}x$.[3]

Accepted Answer

$\dfrac{\sqrt3}{6}$

Sine quotient with a double angle

Sine quotient with a double angle

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