Q.5) Prove the following identities where the angles involved
are acute angles for which the expressions are defined.
EXERCISE 8.4
(ii)
cos A
1
sin A
+
+
1
sin A
+
cos A
=
2 sec A
Proof:
L.H.S
=
cos A
1 + sin A
+
1 + sin A
cos A
=
cos2A
+
(1
+
sin A)2
(1
sin A)
+
.
cos A
=
cos2A
+
1
+
2 sin A
+
sin2A
(1 + sin A) . cos A
=
(sin2A
+
cos2A)
+
1
(1 + sin A) . cos A
+
2sin A
+
(a + b)2 = a2 + 2 ab + b2
=
+
2sin A
(1 + sin A) . cos A
2
Q.5) Prove the following identities where the angles involved
are acute angles for which the expressions are defined.
EXERCISE 8.4
(ii)
cos A
1
sin A
+
+
1
sin A
+
cos A
=
2 sec A
Proof:
L.H.S
=
(1 + sin A) . cos A
=
2
(1
sin A)
+
(1 + sin A) . cos A
2 + 2 sin A
=
2
cos A
=
2
sec A
∴
cos A
1
sin A
+
+
1
sin A
+
cos A
=
2 sec A
L.H.S = R.H.S
∴