untitled

Prove : L.H.S. =
siA

siA

1 n

1 n





=
( 1 n )( 1 n )

( 1 n )( 1 n )

siA siA

siA siA

 

 

=
si A

siA

2

2

1 n

( 1 n )





=
co A

siA

2

2

s

( 1  n )

=
cosA

1 sinA

=
cosA

1

Ñ

coA

siA

s

n

=secAtanA
= R.H.S. (proved).
Example 9. IftanAsinA a and tanAsinA b, prove that, a^2 b^2 4 ab.
Prove : Here given that, tanAsinA a and tanAsinA b
L.H.S. = a^2 b^2
=(tanAsinA)^2 (tanAsinA)^2

= 4 tanAsinA [(ab)^2 (ab)^2 4 ab]

= 4 tan^2 Asin^2 A

= 4 tan^2 A( 1 cos^2 A)

= 4 tan^2 Atan^2 A˜cos^2 A

= 4 tan^2 Asin^2 A

= 4 (tanAsinA)(tanAsinA)

= 4 ab

= R.H.S. (proved)

Activity : 1. If cot^4 Acot^2 A 1 , prove that, cos^4 θcos^2 A 1

2. If sin^2 Asin^4 A 1 , prove that, tan^4 Atan^2 A 1

Example 10. If
2

5

secAtanA , find the value of secAtanA.

Solution: Here given that, .............()
2

5

secAtanA i

We know that, sec^2 A 1 tan^2 A

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†‡‘‹ƒ–‘”„› ( 1 sinA)Ȑ