sin(3x)/sinx +cos(3x)/cosx
=[sin(3x)cosx+cos(3x)sinx]/(sinxcosx)
=sin(3x+x)/[(1/2)sin(2x)]
=2sin(4x)/sin(2x)
=4sin(2x)cos(2x)/sin(2x)
=4cos(2x)
sin(3x)/sinx +cos(3x)/cosx
=[sin(3x)cosx+cos(3x)sinx]/(sinxcosx)
=sin(3x+x)/[(1/2)sin(2x)]
=2sin(4x)/sin(2x)
=4sin(2x)cos(2x)/sin(2x)
=4cos(2x)