Show that cos 20° cos 40° cos 80° = 1/8, and write the product as a decimal.

Step 1. A helpful factor. Call the product $P$. Then $8\sin 20^\circ \cdot P = 8\sin 20^\circ \cos 20^\circ \cos 40^\circ \cos 80^\circ$.

Step 2. Double three times. $2\sin 20^\circ \cos 20^\circ = \sin 40^\circ$, then $2\sin 40^\circ \cos 40^\circ = \sin 80^\circ$, then $2\sin 80^\circ \cos 80^\circ = \sin 160^\circ$. So $8\sin 20^\circ \cdot P = \sin 160^\circ$.

Step 3. Allied angles. $\sin 160^\circ = \sin(180^\circ - 20^\circ) = \sin 20^\circ$. Divide by $8\sin 20^\circ$: $P = \dfrac{1}{8} = 0.125$.