Question

2cos(x/2-П/6)=под корнем 3

Answer 1

2cos(x/2 - pi/6)= корень из 3
2(cos(x/2)cos(pi/6)+sin(x/2)sin(pi/6))=корень из 3
корень из 3*cos(x/2)+(sin(x/2))/2= (корень из 3)/2
Дальше не знаю

Answer 2

To solve the trigonometric equation 2cos(x/2 - π/6) = √3, we need to find the values of x that satisfy the equation. Let's proceed with the solution:

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

Step 2: Identify the angle with a cosine value of √3 / 2: We know that cos(π/6) = √3 / 2.

Step 3: Equate the angles within the cos function: x/2 - π/6 = π/6

Step 4: Solve for x: Add π/6 to both sides: x/2 = π/6 + π/6 x/2 = π/3

Multiply both sides by 2 to isolate x: x = 2 * π/3

So, the solutions to the equation are: x = 2 * π/3 + 2 * k * π

where k is an integer (positive, negative, or zero) that allows for multiple solutions as the cosine function is periodic.