sin²x = 3cos²x + 2sinx*cosx

We know that cos²x = 1 - sin²x, so we can substitute that in:

sin²x = 3(1 - sin²x) + 2sinx*cosx

Expanding:

sin²x = 3 - 3sin²x + 2sinx*cosx

Rearranging terms:

4sin²x - 2sinx*cosx - 3 = 0

Now we can substitute sinx = sin(x) and cosx = cos(x) to make it clearer:

4sin²(x) - 2sin(x)cos(x) - 3 = 0

This is the final equation in terms of sine and cosine functions.