yo 

 3.21 



MATHEMATICAL FORMULA AND ELLIPTIC FUNCTIONS 





sin 1 x = sin"~ 1 ( x) = cos" 1 ^ = cos" 1 AI 



= - - sin" 1 Vi x 2 = + - sin" 1 (2x 2 - i) 

 2 42 



1 x 

 = - cos" 1 (i - 2x 2 ) = tan" 1 . 



2 Vi - X 2 



, I - V I - X 2 I I I 2*V I - 



= 2 tan" 1 \ = - tan" 1 ,< 



2 I - 2X* 



cof 



= j-*log (x + Vx 2 - i) 



3.22 



COS l X = 7T COS" 1 ( #) = Sin" 1 X = COS" 1 (2X 2 I) 



, 4 /I + X 



2 cos" 1 V/ = sin" 1 



tan' 



3.23 



2 tan 



-i 



= - tan- 1 



2 



i 



= cot 



Vi -X 2 



= ^* log (* + Vx 2 - i) = 7T- *' log 



tan" 1 x = - tan- 1 (-#) = sin" 1 = = cos- 



'i + a: 2 Vi + ^ 2 



I . . 2X 7T 



sm 



~ cot * = sec ~ 



7T I I .IX 2 



= tan" 1 - = - cos" 1 5 



2 #2 I + X 2 



2 COS 



, f vr+i? - 



= 2 Sin" 1 - - 



- tan- 1 -^L- = 2 tan" 1 I Vl + ^ - 



2 I X 2 X 



tan" 1 c + tan" 1 



i ex 



2 i + & 2 i x 2* i ix 



