To solve the equation sin(2x) = √3sin(x), we will use the double angle identity for sine, which states that sin(2x) = 2sin(x)cos(x).
So, we have 2sin(x)cos(x) = √3sin(x).
Dividing both sides by sin(x), we get 2cos(x) = √3.
Dividing both sides by 2, we get cos(x) = √3/2.
Now, we know that cos(π/6) = √3/2.
Therefore, x = π/6 + 2nπ or x = 5π/6 + 2nπ, where n is an integer.
To solve the equation sin(2x) = √3sin(x), we will use the double angle identity for sine, which states that sin(2x) = 2sin(x)cos(x).
So, we have 2sin(x)cos(x) = √3sin(x).
Dividing both sides by sin(x), we get 2cos(x) = √3.
Dividing both sides by 2, we get cos(x) = √3/2.
Now, we know that cos(π/6) = √3/2.
Therefore, x = π/6 + 2nπ or x = 5π/6 + 2nπ, where n is an integer.