$2\sin 3\theta \cos\theta$

$2\cos 5\theta \sin 3\theta$

$\sin 5\theta \cos 2\theta$

$2\sin 7\theta \sin 2\theta$

$\cos(x+y)\sin(x-y)$

$\cos(2x+30^\circ)\cos(2x-30^\circ)$

$\sin 12^\circ \sin 46^\circ$

$\sin(x+45^\circ)\sin(x-45^\circ)$

$\sin 5\theta + \sin 3\theta$

$\sin 8\theta - \sin 4\theta$

$\cos 6\theta + \cos 3\theta$

$\cos 7\theta - \cos\theta$

$\cos 12^\circ + \cos 48^\circ$

$\sin(x+30^\circ) + \sin(x-30^\circ)$

$\dfrac{\sin 3x - \sin x}{\cos x - \cos 3x} = \cot 2x$

$\dfrac{\sin 8x + \sin 2x}{\cos 8x + \cos 2x} = \tan 5x$

$\dfrac{\sin A - \sin B}{\sin A + \sin B} = \tan\dfrac{A-B}{2}\cot\dfrac{A+B}{2}$

$\dfrac{\sin 80^\circ + \sin 40^\circ}{\cos 80^\circ + \cos 40^\circ} = \sqrt{3}$

$\cos 15^\circ + \cos 105^\circ + \cos 195^\circ + \cos 160^\circ + \cos 285^\circ = 0$

$\dfrac{\sin 2\theta + \sin 4\theta + \sin 6\theta + \sin 8\theta}{\cos 2\theta + \cos 4\theta + \cos 6\theta + \cos 8\theta} = \tan 5\theta$

$\cos 20^\circ \cos 40^\circ \cos 60^\circ \cos 80^\circ = \dfrac{1}{16}$

$\sin\dfrac{\pi}{9}\sin\dfrac{2\pi}{9}\sin\dfrac{\pi}{3}\sin\dfrac{4\pi}{9} = \dfrac{3}{16}$

$\sin 10^\circ \sin 30^\circ \sin 50^\circ \sin 70^\circ = \dfrac{1}{16}$