To solve the equation sin(x+30°) = sin(2x), we can use the identity sin(A+B) = sin(A)cos(B) + cos(A)sin(B).

Using this identity, we can rewrite the equation as:

sin(x)cos(30°) + cos(x)sin(30°) = sin(2x)

Since sin(30°) = 1/2 and cos(30°) = √3/2, we can substitute these values into the equation:

sin(x)(√3/2) + cos(x)(1/2) = sin(2x)

Multiplying through by 2 to eliminate the denominators, we get:

√3sin(x) + cos(x) = 2sin(2x)

Using the double angle identity sin(2x) = 2sin(x)cos(x), we can simplify further:

√3sin(x) + cos(x) = 2(2sin(x)cos(x))

Expanding the right side of the equation:

√3sin(x) + cos(x) = 4sin(x)cos(x)

Rearranging the terms:

√3sin(x) - 4sin(x)cos(x) + cos(x) = 0

Factoring out sin(x):

sin(x)(√3 - 4cos(x)) + cos(x) = 0

Now we have two possibilities:

1) sin(x) = 0
2) (√3 - 4cos(x)) = 0

For the first possibility, sin(x) = 0, we have x = 0°, 180°, 360°, ...

For the second possibility, (√3 - 4cos(x)) = 0, we can solve for cos(x):

√3 - 4cos(x) = 0
4cos(x) = √3
cos(x) = √3/4

Using the inverse cosine function, we find:

x = arccos(√3/4) ≈ 30°, 330°

Therefore, the solutions to the equation sin(x+30°) = sin(2x) are:

x = 0°, 30°, 180°, 330°, 360°, ...