Question

Ctg(arccos1+2arctg(-√3/3))

Answer 1

Решение задания приложено

Answer 2

I hope this helps you

Answer 3

To solve the given expression, we'll start by simplifying the inner part of the expression step by step and then calculate the final result.

1. arccos(1): The arccosine function returns the angle whose cosine is the given value. Since the range of the arccosine function is [0, π], and cos(0) = 1, we get:

arccos(1) = 0

2. arctg(-√3/3): The arctangent function returns the angle whose tangent is the given value. Since the range of the arctangent function is (-π/2, π/2), and tan(-π/6) = -√3/3, we get:

arctg(-√3/3) = -π/6

Now, let's substitute these values back into the original expression:

Ctg(arccos(1) + 2 * arctg(-√3/3)) = Ctg(0 + 2 * (-π/6))

Since the cotangent function (Ctg) is the reciprocal of the tangent function (tan), we can simplify further:

Ctg(0 + 2 * (-π/6)) = Ctg(-π/3)

Now, let's find the cotangent of -π/3:

cot(-π/3) = 1 / tan(-π/3)

The tangent of -π/3 can be found using the trigonometric identity: tan(-π/3) = -√3

cot(-π/3) = 1 / (-√3) = -1/√3

So, the final result is -1/√3.