Page 2 - LN

2
2
2
PQ + QR = PR
2
Divide each term by QR , we get

PQ 2 QR 2 PR 2
+ =
QR 2 QR 2 QR 2

2
2
tan R + 1 = sec R

+ = .......................2

0
Note:sec θ and tanθare not defined for θ= 90 , So identity 2 is true for all θ such
0
0
that 0 ≤ θ < 90

2
2
2
PQ + QR = PR
2
Divide each term by PQ , we get

PQ 2 QR 2 PR 2
+ =
PQ 2 PQ 2 PQ 2

2
2
1 + cot R = sec R

+ = ...........................3

0
Note:cosec θ and cot θare not defined for θ= 0 , So identity 3 is true for all θ such
0
that 0 < θ ≤ 90 .
0

So, the identities are-

2
2
sin + cos = 1

+ =

+ =

Example1 : Prove that (1 - sin 2 ) sec 2 = 1
2