Final answer:
To solve for 2 cos (π / 6) - cos 2 (π / 6), we use trigonometric identities, ending up with √3 - ½, which simplifies to ½. The correct answer is option c) 1 / 2.
Step-by-step explanation:
The question asks to find the value of 2 cos (π / 6) - cos 2 (π / 6). This problem involves using trigonometric identities. First, let's simplify 2 cos (π / 6), which is equivalent to √3, because cos (π / 6) equals √3/2.
Next, let's evaluate cos 2(π / 6), which can be simplified using the double angle formula cos 2θ = 2 cos² θ - 1. Since cos (π / 6) is √3/2, plugging this into the double angle formula gives us 2 (√3/2)² - 1 = 2(¾) - 1 = ½.
Finally, calculating 2 cos (π / 6) - cos 2 (π / 6), we have √3 - ½, which simplifies to 2√3/2 - ½ = √3 - ½. The correct answer is ½, which corresponds to option c) 1 / 2.