need to prove that (sin(x)+sin(3x))\cos(x)+cos(3x))=tan(2x)

Question

anonymous · Answer

sinx+sin3x=2sin(x+3x)/2cos(x-3x)/2
                  =2sin(4x)/2cos(-2x)/2
                  =2sin2xcos(-x)                      cos(-x)=cosx
                  =2sin2xcosx..............A
cosx+cos3x=2cos(x+3x)/2cos(x-3x)/2
                    =2cos(4x)/2cos(-2x)/2
                    =2cos2xcosx.............B
DIVIDING A by B
(sinx+sin3x)/cosx+cos3x=(2sin2xcosx)/2cos2xcosx
cancelling cosx by cosx & 2 by 2 gives
                                         =sin2x/cos2x
                                         =tan2x

anonymous · Answer

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