Question

prove that (tan A+ sec A)-(sec A+tan A)(sec A-tan A)=(tan A +sec A)(1-(sec A-tan A))

Answer 1

(tanA + secA) - (secA + tanA) ( secA - tanA)
  =  (tanA + secA) - (sec^2 A -  tan^2A)
  = (tanA + secA ) - 1 
**************************************************
(tanA + secA) - (secA + tanA) (secA - tan A)
    = (tanA + secA)  - (tanA + secA) (secA - tanA)   [ (a+b) = (b + a)]
    = (tanA + secA) ( 1 - (secA - tanA) )