Question

2cos(х-п/6)= корень3

Answer 1

2cos⁡(x-π/6)=√3

cos⁡(x-π/6)=√3/2

cos⁡(x-π/6)=√3/2

cos⁡(2π-(x-π/6) )=√3/2

x-π/6=arccos⁡(√3/2)

cos⁡(13π/6- x)=√3/2

x- π/6=π/6

13π/6 - x=arccos⁡(√3/2)

x- π/6=π/6  + 2kπ, k ∈ z

13π/6 - x = π/6

x= π/3+2πk,kϵz

13π/6 - x=π/6+2πk,kϵz

x= π/3+2πk,kϵz

x=2π-2kπ,kϵz

x= π/3+2πk,kϵz

x=0+2πk,kϵz

x= π/3+2πk,kϵz

x=2πk,kϵz

Answer 2

To solve the equation 2cos(x - π/6) = √3, we'll first isolate cos(x - π/6) and then find the value of x.

Step 1: Isolate cos(x - π/6): Divide both sides by 2: cos(x - π/6) = √3 / 2

Step 2: Find the angle that has a cosine value of √3 / 2: The cosine function is positive in the first and fourth quadrants. In the first quadrant, the reference angle with a cosine value of √3 / 2 is π/6. In the fourth quadrant, it's -π/6.

Step 3: Find all solutions for x: To find all solutions for x, we need to consider all possible angles that differ by multiples of 2π. So, the solutions are:

x = π/6 + 2nπ, where n is an integer (for the first quadrant solution) x = -π/6 + 2nπ, where n is an integer (for the fourth quadrant solution)

These equations represent the general solutions for x. You can plug in integer values for n to find specific solutions. Keep in mind that the solutions will repeat every 2π due to the periodic nature of the cosine function.