Question

4cos(x/2+pi/6)+√12=0

Answer 1

Решение задания смотри на фотографии

Answer 2

To solve the equation 4cos(x/2+pi/6)+√12=0, we can start by isolating the cosine term:

4cos(x/2+pi/6) = -√12

Next, we can divide both sides by 4 to get:

cos(x/2+pi/6) = -√3/3

Now, we need to find the angle whose cosine is -√3/3. This angle is -π/6 or 11π/6.

To find all the solutions to the equation, we need to take into account that the cosine function has a period of 2π. Therefore, we need to add integer multiples of 2π to the two angles we found to get all the possible solutions.

So, the solutions to the equation are:

x/2+pi/6 = -π/6 + 2πn or x/2+pi/6 = 11π/6 + 2πn, where n is an integer.

Solving for x, we get:

x = -2π/3 + 4πn - pi/3 or x = 22π/3 + 4πn - pi/3, where n is an integer.

Therefore, the solutions to the equation are:

x = -2π/3 - pi/3 = -5π/3

or

x = 22π/3 - pi/3 = 7π/3

Note that we can add any integer multiple of 4π to these solutions and still get a valid solution to the equation.