#(1+tanA)^2+(1+cotA)^2=(secA+cscA)^2#
#tanA=sinA/cosA#
#cotA=cosA/sinA#
#secA=1/cosA#
#cscA=1/sinA#
#(1+sinA/cosA)^2+(1+cosA/sinA)^2=(1/cosA+1/sinA)^2#
#(cosA+sinA)^2/cos^2A+(sinA+cosA)^2/sin^2A=(sinA+cosA)^2/(sinAcosA)#
#(cosA+sinA)^2(1/cos^2A+1/sin^2A)=(cosA+sinA)^2(1/(sinAcosA))#
#(sin^2A+cos^2A)/(sin^2Acos^2A)=1/(sinAcosA)#
#1/(sinAcosA)^2=1/(sinAcosA)#
#(sinAcosA)^2=sinAcosA#
#(sinAcosA)^2-sinAcosA=0#
#sinAcosA(sinAcosA-1)=0#
#sinA=0, cosA=0, sinAcosA-1=0#
#sinA=0->A=0,pi,2pi,3pi,...#
#cosA=0->A=pi/2,(3pi)/2,(5pi)/2,(7pi)/2,......#
#sinAcosA=0->1/2sin2A=0->sin2A=0#
#2A=0,pi,2pi,3pi,...#
#A=0,pi/2,pi,(3pi)/2,2pi,(5pi)/2,3pi,(7pi)/2,......#
Hence, the values ofA satisfying the equation
#(1+tanA)^2+(1+cotA)^2=(secA+cscA)^2# are,
#A=......,(-7pi)/2,-3pi,(-5pi)/2,-2pi,(-3pi)/2,-pi,-pi/2,0,pi/2,pi,(3pi)/2,2pi,(5pi)/2,3pi,(7pi)/2,......#