=

θ

θ

2

2

1 sin

1 sin





= 1 = R.H.S. (proved)

Example 6. Prove that : 1
2 n

1

2 n

1

si^2 A ta^2 A^

Proof : L.H.S. =
si^2 A 2 tan^2 A

1

2 n

1







=

co A

si A si A

2

2 2

s

n

2

1

2 n

1







=

co A si A

co A

si A^22

2

(^22) s n
s
2 n
1




si A si A
co A
si A^22
2
(^22) ( 1 n ) n
s
2 n
1
 



si A si A
co A
si A^22
2
(^222) n n
s
2 n
1
 



si A
si A
si A^2
2
(^22) n
1 n
2 n
1





A
si A
2
2
2 sin
2 n


= 1 = R.H.S. (proved)
Example 7. Prove that : 0
n
c 1
c 1
n


 taA
seA
seA
taA
proof : L.H.S. =
taA
seA
seA
taA
n
c 1
c 1
n 



seA taA
ta A se A
( c 1 ) n
n^2 ( c^21 )

 
[sec^2 θ 1 tan^2 θ]

seA taA
ta A ta A
( c 1 ) n
n^2 n^2



(secA 1 )tanA
0

= 0 = R.H.S. (proved)
Example 8. Prove that : seA taA
siA
siA
c n
1 n
1 n