(Q16)Show that
1 - tan2 A
cot2 A - 1
= tan2 A

L.H.S. =
1 - tan2 A
cot2 A - 1
=
1
1
-
2 A
2 A
2 A
2 A
-
1
1
[∵ tan A =
sin A
cos A
; cot A =
cos A
sin A
]
=
2 A - 2 A
2 A
2 A - 2 A
2 A
=
2 A - 2 A
2 A
×
2 A
2 A - 2 A
=
2 A
2 A

= 2 A = R.H.S.