First, isolate the cosine term by dividing both sides by 2:
cos(x-π/6) = √3 / 2
Now, recall that cos(π/6) = √3 / 2. Thus, we can rewrite the equation as:
cos(x-π/6) = cos(π/6)
Since the cosine function is an even function, we have:
x-π/6 = π/6 + 2kπ, where k is an integer
Now, solve for x:
x = π/6 + π/6 + 2kπ
x = π/3 + 2kπ
Therefore, the general solution for the equation 2cos(x-π/6) = √3 is:
x = π/3 + 2kπ, where k is an integer.
First, isolate the cosine term by dividing both sides by 2:
cos(x-π/6) = √3 / 2
Now, recall that cos(π/6) = √3 / 2. Thus, we can rewrite the equation as:
cos(x-π/6) = cos(π/6)
Since the cosine function is an even function, we have:
x-π/6 = π/6 + 2kπ, where k is an integer
Now, solve for x:
x = π/6 + π/6 + 2kπ
x = π/3 + 2kπ
Therefore, the general solution for the equation 2cos(x-π/6) = √3 is:
x = π/3 + 2kπ, where k is an integer.