(1+ cot A - cosec A) (1+ tan A + sec A) = 2
(1+cot A -cosec A)(1+ tan A + sec A)
Lhs
=(1 +cos A/sin A - 1/sin A)(1 + sin A/cos A +1/cos A)
=(sin A+cos A -1/sin A)(cos A +sin A+1/cos A)
=(sin A+cos A -1)(sin A+cos A+1)/sin Acos A
=[(sin A+cos A)2-(1)2]/sin Acos A
=[sin2A+cos2A +2sin Acos A - 1]/sin Acos A
=[1-1+2sin Acos A]/sin Acos A
=2sin Acos A/sin Acos A
=2 =Rhs