Please someone help me to prove this.

Step-by-step explanation:

8 cos 80° cos 140° cos 160°

4 (2 cos 80° cos 140°) cos 160°

4 cos 160° (2 cos 80° cos 140°)

Use product to sum formula.

4 cos 160° (cos 60° + cos 220°)

4 cos 160° (½ + cos 220°)

2 cos 160° + 4 cos 220° cos 160°

2 cos 160° + 2 (2 cos 220° cos 160°)

Use product to sum formula again.

2 cos 160° + 2 (cos 60° + cos 380°)

2 cos 160° + 2 (½ + cos 380°)

2 cos 160° + 1 + 2 cos 380°

2 cos 160° + 1 + 2 cos 20°

Use shift identity cos(180 − θ) = -cos θ.

-2 cos 20° + 1 + 2 cos 20°

1

it is a. 4.2 because 7.6-3.4 gets the remaining length of 4.2. i might be wrong but i am pretty sure this is the answer.

step-by-step explanation: