(Q4)Prove that
1 +sec A
sec A
=
sin 2A
1 - cos A

Answer:

L.H.S =
1 +sec A
sec A

=
1
sec A
+
sec A
sec A

= A+1

=
( A+1)( A-1)
(cos A-1)

=
2A - 1
cos A - 1

=
-1(1 - 2A)
-1 (1- cos A)

=
1 - 2A
1 - cos A

[1 - 2A = sin2A]

=
sin 2A
1 - cos A