Page 3 - LN

Solution: L .H.S = ((1 - sin 2 ) sec 2

= cos 2 sec 2 = cos 2
= 1
R.H.S
Therefore L.H.S = R.H.S ( proved)

2
2
Example 2 :Find the value of 9sec A - 9tan A

2
2
Solution:9sec A - 9tan A
2
2
= 9(sec A - tan A)
2
2
= 9(1) ( 1 + tan A = sec A]
= 9

Example 3:
2
2
If tan + cot =2, find the value of tan +cot

Solution: We have,
tan +cot =2
2
(tan + cot ) = 4
2
2
tan + cot + 2tan cot =4
2
2
tan +cot +2 = 4 ( tan .cot =1)
2
2
tan +cot =2

Example 4: If sin + sin 2 = 1, prove that cos 2 + cos 4 = 1

Solution:Given,
sin + sin 2 = 1
sin = 1 - sin 2
sin = cos 2
cos 4 = sin 2 (i)
Now, consider the LHS of equation cos 2 + cos 4 = 1
LHS = cos 2 + cos 4
= cos 2 + sin 2 [from (i)]
= 1 [using cos 2 +sin 2 = 1]
= RHS. ( proved)

NCERT Exercise 8.4

Q. 1. Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.

3