Question

Ctg( arcctg корень из 3 /3)

Answer 1

Ответ:

Это просто, есть маленькая формула

Объяснение:

ctg(arcctg (x) ) = x

Отсюда выходит что ответ на задачу корень из 3/3

Answer 2

Ответ:

√3 /3.

Объяснение:

Первый способ:

сtg( arcctg (√3 /3))

1. arcctg (√3 /3) = π/3.

2. ctg (π/3) = 1/√3 = √3 /3.

Второй способ:

Воспользуемся формулой ctg ( arcctg x) = x. Эта формула проста в понимании. Умножить на 2, а затем разделить на 2. Прибавить 2, а затем вычесть 2. Это всё противоположные по сути действия.

Та же ситуация и в нашем случае.

сtg( arcctg (√3 /3)) = √3/3.

Answer 3

To evaluate the expression Ctg(arcctg(sqrt(3)/3)), let's break it down step by step.

1. Let's start by evaluating arcctg(sqrt(3)/3). The arcctg function is the inverse of the cotangent function, so arcctg(x) returns the angle whose cotangent is x. In this case, we have arcctg(sqrt(3)/3).

To find the angle whose cotangent is sqrt(3)/3, we can use the fact that cot(x) = 1/tan(x). Therefore, cot(arcctg(sqrt(3)/3)) = 1/tan(arcctg(sqrt(3)/3)).

2. Now let's focus on tan(arcctg(sqrt(3)/3)). The tangent of an angle is the ratio of the sine to the cosine of the angle. We can use the Pythagorean identity sin^2(x) + cos^2(x) = 1 to find the missing trigonometric function.

Since cot(x) = 1/tan(x), we can rewrite cot(arcctg(sqrt(3)/3)) as 1/tan(arcctg(sqrt(3)/3)) and substitute cot(x) with 1/tan(x).

Using the Pythagorean identity, we have sin^2(x) + cos^2(x) = 1. Rearranging it, we get cos^2(x) = 1 - sin^2(x). Dividing both sides by cos^2(x), we have 1 = (1 - sin^2(x))/cos^2(x). Simplifying further, we get 1 = 1/cos^2(x) - sin^2(x)/cos^2(x). Since tan(x) = sin(x)/cos(x), we can rewrite it as 1 = 1/cos^2(x) - tan^2(x).

Now, substituting tan(x) = sqrt(3)/3, we have 1 = 1/cos^2(x) - (sqrt(3)/3)^2. Simplifying further, we get 1 = 1/cos^2(x) - 3/9.

Rearranging the equation, we have 1/cos^2(x) = 9/9 - 3/9 = 6/9 = 2/3. Taking the reciprocal of both sides, we get cos^2(x) = 3/2.

Since cos^2(x) is positive, we can take the square root of both sides, which gives us cos(x) = sqrt(3/2). Note that we're taking the positive square root because cos(x) is positive in the fourth quadrant where arcctg(x) lies.

3. Now that we have cos(x) = sqrt(3/2), we can use the identity Ctg(x) = 1/tan(x) to find Ctg(arcctg(sqrt(3)/3)). Substituting tan(x) = sqrt(3)/3, we get Ctg(arcctg(sqrt(3)/3)) = 1/(sqrt(3)/3) = 3/sqrt(3) = sqrt(3).

Therefore, Ctg(arcctg(sqrt(3)/3)) = sqrt(3).