Page 115 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

VED1
E\L-LOVELY-H\math6-1 IInd 21-10-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

bdkbZ vodyu% lkis{k

(
θ j[kus ij uksV

1 + x − 2 1 1 + tan θ 2 − 1
( tan − 1 = tan − 1
x tan θ

( tan − 1 sec θ− 1 = tan − 1 1 − cos θ
tan θ sin θ
2 1
2sin θ
( tan − 1 1 2 1
2 sin θ cos θ
2 2

( tan − 1   tan θ  = θ  = tan − 1 x
2  2  2

dy d  − 1 1 + x − 2 1 
∴ 1 (  tan 
dx dx   x  

d  tan − 1 x  1
( dx   2   = 2 (1 + x 2 )

dy d − 1 1
rFkk 2 ( (tan ) x = 2
dx dx 1 + x
dy d [tan − 1 { 1 − x − 2 1}/ x
∴ 1 (
dy 2 d (tan − 1 ) x
1
2(1 + x 2 ) 1
( = . mÙkj
1 2
1 + x 2

1 32

VkLd
dk vody&xq.kkad

osQ lkis{k ( ij Kkr dhft,A (mÙkj % )
3 5
  2x   2x
mnkgj.k 4- tan −1   dk sin −1  2  osQ lkis{k vody&xq.kkad Kkr dhft,A
 1 − x 2   1+ x 

 2x  − 1  2x 
gy % ekuk ( tan − 1  2  rFkk ( sin  2 
 1 − x   1 +x 
(
θ j[kus ij]
 2tan θ 
( tan − 1   = tan − 1 (tan 2 ) θ = 2θ = 2 tan − 1 x
2
 1− tan θ 
dy 1 1 2
rc ( 2. 2 = 2
dx 1 + x 1 + x