Isabella A.

asked • 05/14/18

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! 
 
 
         

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