Question

Ctgx+1=0 помогите пожалуйста ​

Answer 1

Ответ:

x=$\frac{3\pi }{4} +k\pi$,k∈Z

Объяснение:

ctgx+1=0

ctgx= -1

x=$\frac{3\pi }{4} +k\pi$,k∈Z

Answer 2

Ответ:

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Answer 3

Solving the Equation Ctgx + 1 = 0

To solve the equation Ctgx + 1 = 0, we can use the trigonometric identity for cotangent. The cotangent of an angle is the reciprocal of the tangent of the angle. Therefore, we can rewrite the equation in terms of the tangent function and solve for x.

The cotangent function (cot or ctg) is defined as the ratio of the adjacent side to the opposite side in a right-angled triangle. The cotangent of an angle x is given by the formula: cot(x) = 1 / tan(x).

Using the Trigonometric Identity

We can rewrite the given equation Ctgx + 1 = 0 in terms of the tangent function using the identity cot(x) = 1 / tan(x):

1 / tan(x) + 1 = 0

Now, we can solve for tan(x) by rearranging the equation:

1 = -tan(x)

Finding the Solution

To find the solution for x, we need to find the angle whose tangent is equal to -1. In the standard interval for tangent function (-π/2, π/2), the tangent function is negative in the second and fourth quadrants.

In the second quadrant, the reference angle whose tangent is 1 is π - π/4, and in the fourth quadrant, it is 2π - π/4.

Therefore, the solutions for x are: - x = π - π/4 + 2kπ, where k is an integer for the second quadrant. - x = 2π - π/4 + 2kπ, where k is an integer for the fourth quadrant.

These are the general solutions for the equation Ctgx + 1 = 0.

I hope this helps! If you have any further questions or need additional assistance, feel free to ask.