Question

Cos (pi/6 - 2x)=-1 срочно помогите!!!!))))

Answer 1

cos(Pi/6-2x)=-1

Pi/6-2x=Pi+2Pi*n; n e Z;

-2x=5*Pi/6+2Pi*n; n e Z;

2x=-5*Pi/6-2Pi*n; n e Z;

 

x=-5*Pi/12-Pi*n; n e Z;

Ответ:  x=-5*Pi/12-Pi*n; n e Z;

 

 

 

 

 

 

 

 

Answer 2

Solving the Equation Cos(pi/6 - 2x) = -1

To solve the equation Cos(pi/6 - 2x) = -1, we need to find the values of x that satisfy the equation. Let's break down the steps to solve it:

1. Start with the given equation: Cos(pi/6 - 2x) = -1.

2. We know that Cos(0) = 1. Therefore, we can rewrite the equation as Cos(pi/6 - 2x) = Cos(0).

3. Use the identity Cos(a - b) = Cos(a)Cos(b) + Sin(a)Sin(b) to rewrite the equation as Cos(pi/6)Cos(2x) + Sin(pi/6)Sin(2x) = 1.

4. Simplify the equation using the values of Cos(pi/6) = sqrt(3)/2 and Sin(pi/6) = 1/2: (sqrt(3)/2)Cos(2x) + (1/2)Sin(2x) = 1.

5. Multiply the equation by 2 to eliminate the fractions: sqrt(3)Cos(2x) + Sin(2x) = 2.

6. Rearrange the equation: Sin(2x) + sqrt(3)Cos(2x) = 2.

Now, let's find the solutions for x.

To solve this trigonometric equation, we can use the trigonometric identity Sin^2(x) + Cos^2(x) = 1.

Let's square both sides of the equation Sin(2x) + sqrt(3)Cos(2x) = 2:

(Sin(2x))^2 + 2Sin(2x)sqrt(3)Cos(2x) + 3(Cos(2x))^2 = 4.

Using the identity Sin(2x) = 2Sin(x)Cos(x) and Cos(2x) = Cos^2(x) - Sin^2(x), we can rewrite the equation as:

(2Sin(x)Cos(x))^2 + 2(2Sin(x)Cos(x))sqrt(3)(Cos^2(x) - Sin^2(x)) + 3(Cos^2(x) - Sin^2(x))^2 = 4.

Simplifying further:

4Sin^2(x)Cos^2(x) + 4sqrt(3)Sin(x)Cos^3(x) - 4sqrt(3)Sin^3(x)Cos(x) + 3Cos^4(x) - 6Cos^2(x)Sin^2(x) + 3Sin^4(x) = 4.

Rearranging the terms:

3Sin^4(x) + 4Sin^2(x)(Cos^2(x) - 2) + 3Cos^4(x) + 4sqrt(3)Sin(x)Cos^3(x) - 4sqrt(3)Sin^3(x)Cos(x) - 4 = 0.

This equation is a quartic equation in terms of Sin(x) and Cos(x). Solving quartic equations can be complex and may require numerical methods or approximations.

Unfortunately, I couldn't find a specific solution for the equation Cos(pi/6 - 2x) = -1. It seems to be a complex equation that may require further analysis or numerical methods to find the exact solutions.

Please note that the equation may have multiple solutions, and it's always a good idea to verify the solutions by substituting them back into the original equation.

I hope this explanation helps! If you have any further questions, please feel free to ask.