Page 116 - DECO403_MATHEMATICS_FOR_ECONOMISTS_HINDI

VED1
E\L-LOVELY-H\math6-1 IInd 6-8-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

vFkZ'kkfL=k;ksa dk xf.kr

uksV  2tan θ 
rFkk ( sin − 1   = sin − 1 (sin 2 ) θ = 2θ = 2 tan − 1 x
 1+ tan θ 
2

dy 2 1 2
rc ( 2. 2 = 2
dx 1 + x 1 + x

dy 1 d [tan − 1 {2 /(1 − x 2 )}]
x
∴ dy 2 ( d [sin − 1 {2 /(1 + x 2 )}]
x
d − 1 2
x
dx [tan {2 /(1 − x )}]
( d − 1 2
x
dx sin {2 /(1 + x )}

2 1 + x 2
( 1 + x 2 × 2 = 1. mÙkj

-1
mnkgj.k 5- iQyu sin (2x 1 − x dk
osQ lkis{k vody&xq.kkad Kkr djsaA

gy % ekuk ( sin − 1 2x 1 − x 2

(

θ

θ
θ
( sin − 1 (2sinθ 1 − sin θ 2 ) = sin − 1 (2sin cos )

θ
( sin − 1 (sin 2 )

( θ (

dy 1 2
dx ( 1 − x 2

iqu% (

dy 2 1
dx ( 1 − x 2

2
d sin − 1 (2x 1 − x 2 ) 1 − x 2
rc − 1 ( = 2. mÙkj
d sin x 1
1 − x 2

dy x 2 1 − y 6
mnkgj.k 6- ;fn 1 − 6 + x − 1 y 6 a 3 (x 3 − y 3 ) gks] rks fl¼ dhft, dx = y 2 1 − x 6 -

gy % ekuk (

θ) (

φ) rc 1 − x + 6 1 − y = 6 a 3 (x − 3 y 3 )