| $\frac{5\pi}{6}$ | $\times$ | $\frac{2\pi}{3}$ | $\times$ | $0$ | $=1$ |
| $\times$ | $\times$ | $\times$ | |||
| $\frac{\pi}{6}$ | $\times$ | $\sin{\frac{\pi}{4}}$ | $\times$ | $\frac{3\pi}{4}$ | $=-\frac{1}{4}$ |
| $\times$ | $\times$ | $\times$ | |||
| $\frac{5\pi}{6}$ | $\times$ | $\frac{\pi}{2}$ | $\times$ | $\frac{3\pi}{4}$ | $=0$ |
| $\parallel$ | $\parallel$ | $\parallel$ | |||
| $\frac{1}{4}$ | $0$ | $-\frac{1}{2}$ |
Evaluate:
a) $\displaystyle\sin{\left(\frac{\pi}{2}-\theta\right)}+\sin{\left(\pi-\theta\right)}-\cos{\left(\frac{\pi}{2}-\theta\right)}+\cos{\left(\pi-\theta\right)}$
b) $\displaystyle\frac{1-\sin{\left(\pi-\theta\right)}}{1+\sin{\left(\frac{\pi}{2}-\theta\right)}}\times\frac{1-\cos{\left(\pi-\theta\right)}}{1-\cos{\left(\frac{\pi}{2}-\theta\right)}}$
Simplify the following to a single fraction:
$\displaystyle\frac{1-\sin{x}-\cos{x}}{1-\sin{x}+\cos{x}}+\frac{1+\sin{x}+\cos{x}}{1+\sin{x}-\cos{x}}$