Question

[2 cos ( - π/3)]² - 4 [ctg (-π/6)]

Answer 1

(2cos(-π/3))² - 4ctg(-π/6) = (2 · 1/2)² + 4ctgπ/6 = 1 + 4 · √3 = 4√3 + 1

Answer 2

To simplify the given expression, let's start by evaluating the trigonometric functions:

1. cos(-π/3) = cos(-60°) = 1/2
2. ctg(-π/6) = ctg(-30°) = 1 / tan(-30°) = 1 / (-√3) = -√3 / 3

Now, plug these values back into the original expression:

[2 * cos(-π/3)]^2 - 4 * [ctg(-π/6)] = [2 * (1/2)]^2 - 4 * (-√3 / 3) = (1)^2 - 4 * (-√3 / 3) = 1 + 4 * (√3 / 3) = 1 + 4√3 / 3 = (3 + 4√3) / 3

So, the simplified form of the expression is (3 + 4√3) / 3.