$\sin\alpha = \dfrac{3}{5}$

$\cos\alpha = \dfrac{4}{5}$, where $0 < \alpha < \dfrac{\pi}{2}$

$\cot\alpha - \tan\alpha = 2\cot 2\alpha$

$\dfrac{\sin 2\alpha}{1 + \cos 2\alpha} = \tan\alpha$

$\dfrac{1 - \cos\alpha}{\sin\alpha} = \tan\dfrac{\alpha}{2}$

$\dfrac{\cos\alpha - \sin\alpha}{\cos\alpha + \sin\alpha} = \sec 2\alpha - \tan 2\alpha$

$\sqrt{\dfrac{1 + \sin\alpha}{1 - \sin\alpha}} = \dfrac{\sin\dfrac{\alpha}{2} + \cos\dfrac{\alpha}{2}}{\sin\dfrac{\alpha}{2} - \cos\dfrac{\alpha}{2}}$

$\dfrac{\operatorname{cosec}\theta + 2\operatorname{cosec} 2\theta}{\sec\theta} = \cot\dfrac{\theta}{2}$

$1 + \tan\alpha \tan 2\alpha = \sec 2\alpha$

$\dfrac{2\sin\theta \sin 2\theta}{\cos\theta + \cos 3\theta} = \tan 2\theta \tan\theta$

$\dfrac{\sin 3\theta}{\sin\theta} - \dfrac{\cos 3\theta}{\cos\theta} = 2$

$\dfrac{\cos 3\theta}{\cos\theta} + \dfrac{\sin 3\theta}{\sin\theta} = 4\cos 2\theta$

$\dfrac{\tan\dfrac{\theta}{2} + \cot\dfrac{\theta}{2}}{\cot\dfrac{\theta}{2} - \tan\dfrac{\theta}{2}} = \sec\theta$

$\dfrac{\sin 3\theta}{\cos\theta} + \dfrac{\cos 3\theta}{\sin\theta} = 2\cot 2\theta$

$\dfrac{3 + \cos 4\theta}{1 - \cos 4\theta} = \dfrac{1}{2}(\tan^2\theta + \cot^2\theta)$

$\dfrac{1 + \sin 2\theta}{1 - \sin 2\theta} = \tan\left(\dfrac{\pi}{4} + \theta\right)$

$\cos^2\dfrac{\pi}{8} + \cos^2\dfrac{3\pi}{8} + \cos^2\dfrac{5\pi}{8} + \cos^2\dfrac{7\pi}{8} = 2$

$18^\circ$

$36^\circ$

$54^\circ$

$72^\circ$