Hello,

I don't know your method...

Here's how I'd do :

Let's go back to your equation. You can rewrite it this way :

3sin(2x)+2=4cos(2x)

Square the equation :

9sinē(2x)+12sin(2x)+4=16cosē(2x)

Substituting cosē(2x) by 1-sinē(2x), we have :

9sinē(2x)+12sin(2x)+4=16-16sinē(2x)

25sinē(2x)+12sin(2x)-12=0

Factor this out and find sin(2x)