Question

The value of \( \cos 26^\circ + \cos 54^\circ + \cos 126^\circ + \cos 206^\circ + \cos 240^\circ \) is:

• A. 0
• B. 1
• C. \(-\frac{1}{2}\)
• D. \(-\frac{1}{2}\)
• E. -1

Hint:

When dealing with multiple cosines of equally spaced angles, they can often be simplified using known sum formulas or geometric properties.

Answer 1

The Correct Option is C

The expression involves cosines of multiple angles. Using the properties of trigonometric identities, particularly that the sum of cosines of equally spaced angles results in zero or half values, we can simplify the terms. 
Step 1: These cosines can be combined in a sum, recognizing the symmetry about 180 degrees. 
The sum turns out to be: \[ \cos 26^\circ + \cos 54^\circ + \cos 126^\circ + \cos 206^\circ + \cos 240^\circ = -\frac{1}{2} \]