Asked by JD
                I did post it wrong.
sin(4x)/sin(x)=4cos(x)cos(2x).
Verify the identity, please explain!
            
        sin(4x)/sin(x)=4cos(x)cos(2x).
Verify the identity, please explain!
Answers
                    Answered by
            Ms. Sue
            
    Please, keep the same name when posting on Jiskha.
    
                    Answered by
            drwls
            
    It has already been explained. See Reiny's answer to your previous post.
    
                    Answered by
            MathMate
            
    For the left hand side, use
sin(4x)=2sin(2x)cos(2x)
sin(2x)=2sin(x)cos(x)
cos(2x)=cos²(x)-sin²(x)
and finally to eliminate sin²(x), use
sin²(x)=1-cos²(x)
For the right hand side, use
cos(2x)=cos²(x)-sin²(x)
and
sin²(x)=1-cos²(x)
Both sides will be expressed in terms of cos(x).
    
sin(4x)=2sin(2x)cos(2x)
sin(2x)=2sin(x)cos(x)
cos(2x)=cos²(x)-sin²(x)
and finally to eliminate sin²(x), use
sin²(x)=1-cos²(x)
For the right hand side, use
cos(2x)=cos²(x)-sin²(x)
and
sin²(x)=1-cos²(x)
Both sides will be expressed in terms of cos(x).
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