(Q15)Show that √
1 + sin A
1 - sin A
 = sec A + tan A

Given that L.H.S. = √
1 + sin A
1 - sin A

Rationalise the denominator, rational factor of 1 – sin A is 1 + sin A.

= √
1 + sin A
1 - sin A
 ×
1 + A
1 + A
= √
(1 + A)2
1 - 2 A

[∵ (a + b)(a + b) = (a + b)2]; (a – b)(a + b) = a2 — b2]

= √
(1 + A)2
2 A
=
1 + A
A
=
1
A
 +
A
A

= A + A = R.H.S.