Prove that ??(Sinx+Sin2x+Sin3x)/(cosx+cos2x+cos3x) = tan2x

1 Answer
May 11, 2018

LHS=(sinx+sin2x+sin3x)/(cosx+cos2x+cos3x)

=(2sin((3x+x)/2)*cos((3x-x)/2)+sin2x)/(2cos((3x+x)/2)*cos((3x-x)/2)+cos2x

=(2sin2x*cosx+sin2x)/(2cos2x*cosx+cos2x)

=(sin2xcancel((1+2cosx)))/(cos2xcancel((1+2cosx)))

=tan2x=RHS