Mclauren Series for the given functions:
sinx=x-x^3/6+x^5/120-....
inv_sinx=x+x^3/6+3/40x^5+....
tanx=x+x^3/3+2/15 x^5+ ....
inv_tanx=x-x^3/3+x^5/5-....
sinx*inv_sinx=x^2+1/6x^4-1/6x^4+3/40x^6+1/120x^6-1/36x^6+...
sinx*inv_sinx-x^2=3/40x^6+1/120x^6-1/36x^6+...So,
Lt(y->0)(sin-1 y * sin y – y2)/y^6 = 3/40+1/120-1/36 = 1/18

tanx*inv_tanx-x^2=1/5x^6+2/15x^6 -1/9x^6+.....
Lt(y->0) (tan-1 y * tan y – y2)/y^6 = 1/5+2/15-1/9=2/9

Edited on June 3, 2008, 7:32 am

Posted by Praneeth on 2008-06-03 04:08:08