Final answer:
The given expression cos 100 cos 120 cos 140 cos 160 can be simplified using the cosine identity. Applying the identity step by step, we can evaluate the expression to be 0.7327.
Step-by-step explanation:
The given expression is:
cos 100 cos 120 cos 140 cos 160
To simplify this expression, we can use the identity:
cos A cos B = (1/2)(cos(A - B) + cos(A + B))
Using this identity, we can rewrite the expression as:
(1/2)(cos(20) + cos(240))(1/2)(cos(40) + cos(280))
Next, we apply the same identity to cos(20) and cos(40), and then to cos(240) and cos(280):
(1/4)(cos(-20) + cos(60) + cos(-40) + cos(80))
Simplifying further, the expression becomes:
1/4(cos(-20) + cos(60) + cos(-40) + cos(80))
Finally, we can evaluate the cosine values:
1/4(0.9397 + 0.5 + 0.766 + -0.173)
Adding these values together, the result is:
0.7327