Question

Пожалуйста, помогите решить: cos(2x-pi/3)=√2/2 спасибо заранее

Answer 1

2x-π/3=+-π/4+2πk
2x=+-π/4+2πk+π/3
x=+-π/8+πk+π/6   k∈Z

Answer 2

Solving the Equation cos(2x-π/3) = √2/2

To solve the equation cos(2x-π/3) = √2/2, we can use the inverse cosine function to find the value of x. The inverse cosine function, denoted as arccos or cos^-1, gives us the angle whose cosine is a given value. In this case, we want to find the value of x for which cos(2x-π/3) equals √2/2.

Using the inverse cosine function, we can express the solution as: 2x - π/3 = arccos(√2/2)

Now, let's find the value of arccos(√2/2) and solve for x.

The value of arccos(√2/2) is π/4. Therefore: 2x - π/3 = π/4

Solving for x: 2x = π/4 + π/3 2x = 3π/12 + 4π/12 2x = 7π/12

Finally, solving for x: x = 7π/24

So, the solution to the equation cos(2x-π/3) = √2/2 is: x = 7π/24