How to simplify trigonometric equations? (see details of question!)
This is the questions I'm stuck on:
Solve algebraically: f(x) = g(x) when f(x) = 4sin(2x)cos(2x)+2 and g(x)= 4sin(3x)sin(2x) + 2
1. I equated the equations
4 sin(2x)cos(2x)+2 = 4sin(3x)sin(2x) + 2
2. I simplified the equation
sin(2x)cos(2x)+2 = sin(3x)sin(2x) + 2
sin(2x)cos(2x) = sin(3x)sin(2x)
cos(2x) = sin(3x)
3. Now I go on to solve cos(2x) = sin(3x)
BUT the answers say there is a SECOND EQUATION to solve: sin(2x) = 0
I thought I canceled sin(2x) out when I simplified the equation, so I wouldn't have to deal with it.
Please help me understand why this equation is important, and moreover, why it is equal to 0!
I can solve the rest of the question, I understand how to do that, but really need help understanding where the sin(2x) = 0 comes from! Thank you!