Question

√3 cos^2 п/12 - √3 sin^2 п/12

Answer 1

Вынесите корень из 3 за скобку, а остальное сверните по формуле косинуса двойного угла. Получите ответ: - 1,5

Answer 2

We can use the trigonometric identity cos(2θ) = cos^2θ - sin^2θ to simplify the expression.

Let's start by applying the identity to each term of the expression:

cos(π/6) = cos(2π/12) sin(π/6) = sin(2π/12)

Substituting these values, we get:

√3 cos^2(π/12) - √3 sin^2(π/12) = √3 [cos^2(2π/12) - sin^2(2π/12)] (using the identity) = √3 [cos^2(π/6) - sin^2(π/6)] = √3 [cos^2(30°) - sin^2(30°)] (converting to degrees) = √3 [(√3/2)^2 - (1/2)^2] (using the values of cos(30°) and sin(30°)) = √3 [(3/4) - (1/4)] = √3 (1/2) = √3/2

Therefore, √3 cos^2(π/12) - √3 sin^2(π/12) = √3/2.