SEC^2 A-SEC^2 B/(TAN A-TAN B)
=[(TAN^2 A+1)-(TAN^2 B+1)]/(TAN A-TAN B)
=(TAN^2 A-TAN^2 B)/(TAN A-TAN B)
=[(TAN A+TAN B)(TAN A-TAN B)]/(TAN A-TAN B)
=TAN A+TAN B
SEC^2 A-SEC^2 B/(TAN A-TAN B) =[(TAN^2 A+1)-(TAN^2 B+1)]/(TAN A-TAN B) =(TAN^2 A-TAN^2 B)/(TAN A-TAN B) =[(TAN A+TAN B)(TAN A-TAN B)]/(TAN A-TAN B) =TAN A+TAN B