Given:
(1+tanAtanB)2+(tanA−tanB)2
=1+2tanAtanB+tan2Atan2B+tan2A−2tanAtanB+tan2B
=1+tan2A+tan2Atan2B+tan2B
=sec2A+tan2B(tan2A+1)
=sec2A+tan2Bsec2A
=sec2A(1+tan2B)
=sec2Asec2B
(1+tanA tanB)2+(tanA − tanB)2sec2A sec2B= ___