(Q18)Simplify sec A (1 – sin A) (sec A + tan A)

L.H.S. = sec A (1 – sin A) (sec A + tan A)

= ( A – A . sin A) (sec A + tan A)

= ( A -
1
A
 . sin A) (sec A + tan A)

= ( A – A) (sec A + tan A)

= 2 A – 2 A [∵ sec2 A – tan2 A = 1]

=