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OpenStudy (anonymous):

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

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OpenStudy (anonymous):

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

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