#RHS=1-sin^2x/(1+cotx)-cos^2x/(1+tanx)#
#=1-sin^3x/(sinx+sinxcotx)-cos^3x/(cosx+cosxtanx)#
#=1-(sin^3x/(sinx+cosx)+cos^3x/(cosx+sinx))#
#=1-((sin^3x+cos^3x)/(cosx+sinx))#
#=1-((sinx+cosx)(sin^2x-sinxcosx+cos^2x))/(cosx+sinx)#
#=1-(sin^2x-sinxcosx+cos^2x)#
#=1-(1-sinxcosx)#
#=sinxcosx#
But #LHS=1-sinxcosx#
Hence #LGS!=RHS#
So it must be an equation which is
#1-sinxcosx=sinxcosx#
#=>2sinxcosx=1#
#=>sin2x=sin(pi/2)#
#=>2x=npi+(-1)^n(pi/2)#
#=>x=(npi)/2+(-1)^n(pi/4)" where "n in ZZ #