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Prove that (sin(x)+sin(3x))\cos(x)+cos(3x))=tan(2x)

User Gosha A
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sinx+sin3x=2sin(x+3x)/2cos(x-3x)/2                  =2sin(4x)/2cos(-2x)/2                  =2sin2xcos(-x)                      cos(-x)=cosx                  =2sin2xcosx..............Acosx+cos3x=2cos(x+3x)/2cos(x-3x)/2                    =2cos(4x)/2cos(-2x)/2                    =2cos2xcosx.............BDIVIDING A by B(sinx+sin3x)/cosx+cos3x=(2sin2xcosx)/2cos2xcosxcancelling cosx by cosx & 2 by 2 gives                                         =sin2x/cos2x                                         =tan2x
User Matt Coarr
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