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Solving Nonlinear Transcedental equations


I got a problem with Mathematica 5.1 ,as i am going to solve a Nonlinear
Transcedental Equations, which are five variables with five eqations.it is
not able to solve the problem and it is not showing any thing can any
on please solve the problem using mathematica 5.1.
and send me how to solve in mathematica 5.1
The problem statement is

solving the 5 simultaneous Non linear Transcedental equations

cos(5a)+cos(5b)+cos(5c)+cos(5d)+cos(5e)=0
 cos(7a)+cos(7b)+cos(7c)+cos(7d)+cos(7e)=0
 cos(11a)+cos(11b)+cos(11c)+cos(11d)+cos(11e)=0
 cos(13a)+cos(13b)+cos(13c)+cos(13d)+cos(13e)=0
 cos(a)+cos(b)+cos(c)+cos(d)+cos(e)=4

solve for a= ?,b= ?,c= ?,d= ?

thanks
shaym



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