Solving trigonometric /hyperbolic equation using symbolic math toolbox

I am trying to find roots of the equation:

 cosh(x)*cos(x)+1 = 0

I try 2 methods using symbolic math one is using solve function and other using poles function

1)

>> syms x
>> solve((1+cos(x)*cosh(x))==0)

ans =

-212.05750411731104359622842837137

2)

>> poles(1/(1+cosh(x)*cos(x)),x,0,20*pi)

Warning: Cannot determine the poles. 
> In sym.poles at 106 

ans =

[ empty sym ]

I know that the answer is

x = ±1.87510406871196...

x = ±4.69409113297417...

x = ±7.85475743823761...

x = ±10.9955407348755...

ans so on...

When I substitute x = -212.05750411731104359622842837137 in the equation it is not satisfied.

Why can't I get the values of x in the defined range using symbolic math? what do i need to correct in my code?

Thanks

Trupti

PS : I am using Matlab 2012b

[RahulTandon]

do you mind a grafical answer to your problem? it gives a clear answer!

syms x; clf; ezplot('cosh(x)+cos(x)+1'); grid on;

Answer 1

[chadi cream]

k=100; S=zeros(k,1);

for n=1:k sol=vpasolve((1+cos(t)*cosh(t))==0,'random', true); S(n,1)=sol; end S=unique(S) S=sort(S)

Answer 2

[Walter Roberson]

This is the defined behaviour for solve(): when numeric values have to be returned then unless the equation is a polynomial, only a single answer will be returned.

To find numeric roots within a particular range, use vpasolve(). You might have to call it repeatedly to find multiple roots in the range.