Question

Ctg (x+1/2)= корень 3

Answer 1

$ctg(x+ \frac{1}{2})= \sqrt{3} \\ \\ x+ \frac{1}{2}=arcctg \sqrt{3}+\pi n \\ \\ x+ \frac{1}{2}= \frac{\pi}{6}+\pi n \\ \\ \boxed {x= \frac{\pi}{6}- \frac{1}{2}+\pi n,\;\;n \in Z }$

Answer 2

It seems like you have an equation involving the cotangent function and a square root. To better understand the equation, I'll rewrite it for clarity:

Ctg(x + 1/2) = √3

First, let's find the value of x that satisfies this equation.

The cotangent function (ctg) is the reciprocal of the tangent function:

ctg(x) = 1 / tan(x)

So, we can rewrite the equation as:

1 / tan(x + 1/2) = √3

Now, we can simplify the equation further:

tan(x + 1/2) = 1 / √3

To find the value of x, we can take the inverse tangent (arctan) of both sides:

x + 1/2 = arctan(1 / √3)

Now, let's calculate the arctan(1 / √3):

arctan(1 / √3) ≈ 30 degrees ≈ π/6 radians

Now, we can solve for x:

x = π/6 - 1/2 ≈ π/6 - 3/6 ≈ -2/6

So, the value of x that satisfies the equation is approximately -1/3 radians (or approximately -19.1 degrees).