## Trigonometry (11th Edition) Clone

$\theta = 45˚, 135˚,225˚, 315˚$
$\tan \theta - \cot \theta = 0$ $\frac{\sin \theta}{\cos \theta} - \frac{\cos \theta}{\sin \theta} = 0$ $\frac{(\sin \theta)^{2}- (\cos \theta)^{2}}{\cos \theta \sin \theta} = 0$ $(\sin \theta)^{2}- (\cos \theta)^{2} = 0$ $-[-(\sin \theta)^{2}+ (\cos \theta)^{2}] = 0$ $-[(\cos \theta)^{2}-(\sin \theta)^{2}] = 0$ $-cos(2\theta) = 0$ $cos(2\theta) = 0$ (Since its $2\theta$, then its for 2 cycles) $2\theta = 90˚, 270˚, (90˚ + 360˚), (270˚ + 360˚)$ $2\theta = 90˚, 270˚, 450˚, 630˚$ $\theta = \frac{90}{2}˚, \frac{270}{2}˚, \frac{450}{2}˚, \frac{630}{2}˚$ $\theta = 45˚, 135˚,225˚, 315˚$