#(2sinx)/sin(3x)+tanx/tan(3x)=(2sinx)/sin(3x)+(sinx/cosx)/(sin(3x)/cos(3x))=#
#=((2sinx)/cos(3x)+(sinx/cosx)*(sin(3x)/(cos(3x))) ) /(sin(3x)/cos(3x))=#
#=(((2sinxcosx+sinx*(sin(3x)))/(cancelcos(3x)*cosx)) ) /(sin(3x)/cancelcos(3x))=#
#=(( 2sinxcosx+sinx*(sin(3x)) )/cosx)/(sin(3x))=#
#= (2sinxcosx+sinx*sin(3x))/(sin(3x)cosx)=#
#sin(3x)=3sinx-4sin^3x#
#= (2sinxcosx+sinx*sin(3x))/((3sinx-4sin^3x)cosx)=#
#= (cancel(sinx)(2cosx+sin(3x)))/(cancel(sinx)(3-4sin^2x)cosx)=#
#= (2cosx+sin(3x))/((3-4sin^2x)cosx)#