Answer
$\cos$ 100$^{\circ}$$\cos$ 80$^{\circ}$ - $\sin$ 100$^{\circ}$$\sin$ 80$^{\circ}$ $\approx$ 0.99999999
or
$\cos$ 100$^{\circ}$$\cos$ 80$^{\circ}$ - $\sin$ 100$^{\circ}$$\sin$ 80$^{\circ}$ $\approx$ 1
Work Step by Step
$\cos$ 100$^{\circ}$$\cos$ 80$^{\circ}$ - $\sin$ 100$^{\circ}$$\sin$ 80$^{\circ}$
Evaluate each piece:
$\cos$ 100$^{\circ}$ $\approx$ -0.17364818
$\cos$ 80$^{\circ}$ $\approx$ 0.17364818
$\sin$ 100$^{\circ}$ $\approx$ 0.98480775
$\sin$ 80$^{\circ}$ $\approx$ 0.98480775
Combine:
$\cos$ 100$^{\circ}$$\cos$ 80$^{\circ}$ $\approx$ -0.03015369
$\sin$ 100$^{\circ}$$\sin$ 80$^{\circ}$ $\approx$ 0.96984630
-0.03015369 - 0.96984630 $\approx$ 0.99999999
Therefore:
$\cos$ 100$^{\circ}$$\cos$ 80$^{\circ}$ - $\sin$ 100$^{\circ}$$\sin$ 80$^{\circ}$ $\approx$ 0.99999999
or
$\cos$ 100$^{\circ}$$\cos$ 80$^{\circ}$ - $\sin$ 100$^{\circ}$$\sin$ 80$^{\circ}$ $\approx$ 1
